«:   C  V' 

c    < 


vs*^ 

^»<Tkr  c    .    . 

•    <     i.  «••  c    < 

•  '  <o      r     ( 


«: 
<  <       «c.  <  <  « 

<? 

i 


<.    <    .    . 

<.  <c         C        <• 


C   c.          CC          C  C  <f_ 

c  <  «C 

<  <  OC 

c  < 


"    <*    ~  -   <C 

<" 

-  <*  c  '•*  «: 
<       c     v<c  «-    .  <£L 


»-  *. 

c.          < 


*      7* 


•r 


C       <Z 


-     .       at 

t  <     «:        < 


r  .  <     c 
<     <sr  c     c 


-  Cw*d 

£•<:"•<       < 


<:  <      < 


< 


«c  < 

«    .  O»  i 
<c    . 

«• 

-C  co' 

^<    •  <.<:• 

cc  <^- 

• "  <-«^ 

cc  <<1 

.«  .  <  — 

«  «T". 


*>-        «T    •     ' 

•.fK.^-.C?^     •• 
" 


<!•  •       o  «  c 

'«!•       ^   <  < 


•C  <v,     < 


<T'  «r     < 
C:     < 


-«£    ^ 

•« 

•  '•'<«' 

,     <-<t*iK*F 

c*  <^ 

'    <^        Gtt'V 


<r 

• 


-   c 


•<t      ^ 

«r      <  c 
1^ 


i  "       «^\ 

^ — 


<«:_      •  << 


-  «c_      « 


•<*(r"^ 


»1":  *> 

"     <'<       ij*)».<f . 

?•**  ?        > 


^••r.,-.*  .'<»• 


U  .     »»..  '- 

<:      •<      v,.'<^     <f 

c     *     •   .-«:?.  •  *V 


ftpftM 


LIBRARY 


UNIVERSITY  OF  CALIFORNIA. 


Deceived 


Accessions  No.' 


"*  /"^       '  ""    rv  '  ^ 

'-•  '  -  -  -  .-    '^      '• 


*H3WS5i 


t        .Art.    <5f 


n^/9A' 


,  „-  —  I 


wr^r^Mi 


tCTn^«6A^ 


-  ~  ~  -  - 


W^^^-^-:^ . 


^ 


'T/TAnhftfa*fa 

WHWH&i^W. 


III. 


POSITIONS 


FUNDAMENTAL    STARS 


HKIHTF.II    KICoM 


OBSERVATIONS  MADE  AT  THE  U.  S.  NAVAL  OBSERVATORY 


nr.nvKKN  TIIK 


YEARS    1863    ANI)    1867 


SIMON    NEWOOMIl. 


OK     MATHEMATICS.     V.     S.     SAW 


!'Kl:i'Ai:r.|i   AT  THE 


U.    S.    NAVAL    OBSERVATORY 

IIV  OIIUKK  OK 

COMMODORE  15.   I\  SANDS,  U.  S.  N.. 


-  1  ri:  ii  I  XTKN  in.  N  i 


UJIV1RSIT7 


W  ASHING/TON: 

<:  (i  VK17NMEXT     V  R  I  / T  I  N  fi     OFFICK. 

187/. 


TABLE  OF  CONTENTS. 


CHAPTER  I.— EIGHT  ASCENSIONS. 

Page. 

>>stcni;itic  errors  to  which  concluded  right  ascensions  are  liable 5 

Plan  lor  el  i  mi  until  it;  these  •  errors 7 

Kate  of  tin1  Kescels  clock 7 

Kffcct  of  temperature  on  this  rate 7 

Kllect  of  the  barometric  pressure 10 

I '.Meet  of  the  galvanic  current 10 

Magnitude  of  the  irregularities  of  clock  rate 1(1 

Mode  of  detecting  the  systematic  errors  of  the  adopted  star  positions 10 

Formation  of  the  ei| nations  of  condition 11 

Solutions  of  the  equations 18 

Discussion  of  the  results 19 

( 'Directions  to  the  position  of  the  equinox  and  the  obliquity  of  the  ecliptic 5JO 

Concluded  systematic  correct  ion  to  the  adopted  positions  of  the  clock  stars 21 

Comparison  of  right  ascensions  observed  directly  and  by  rcllection  22 

Computation  of  corrections  to  the  right  ascensions  of  the  standard  stars 22 

Discussion  of  differences  between  the  results  of  the  transit  anil  circle  26 

Hight  ascensions  of  I'olaris 2r 

CHAPTER  11.— POLAli  DISTANCES. 

Preliminary  remarks  on  measured  polar  distances 33 

Individual  results  for  corrections  to  polar  distances  of  stars 38 

Concluded  mean  positions  of  standard  st  a  rs  for  the  epoch  1870.0 :FJ 

Comparison  of  the  preceding  polar  distances  with  those  of  other  catalogues 43 

K'emarks  on  these  comparisons 45 


POSITIONS  OF  1TNDAMENTAL  STARS    ftTIXyiBSZTH 
OBSERVATIONS  .MADE  AT  THE  UNITED  STATES  NAVAL  OBSERVATORY 


YEAKS    ISOJi    TO    1867,    INCLUSIVE. 


CHAPTER    I. 

11IGIIT    ASCENSIONS. 

Tin-  agreement  between  the  right  ascensions  of  (lie  fundamental  stars,  resulting  from  tin- work 
•  if  tin-  different  e>hscrvate»ries,  which  have  of  late  years  made  them  a  subject  of  regular  observation, 
is  very  close,  and  well  illustrates  tlie  approach  to  perfection  which  the  art  of  practical  astronomy 
has  made.  Still,  the  small  outstanding  differences  are  greater  than  can  result  from  the  chance 
errors  of  individual  observations,  thus  indicating  that  hidden  sources  of  systematic  error  still  exist. 
A  classiiication  of  the  differences,  with  respect  to  the,  positions  of  the  stars,  show  that  they  arc 
mainly  a  function  of  this  element.  In  fixing  the  positions  of  the  stars,  one  of  tiie  efforts  of  the 
astronomer  will  be  to  look  for  and  eliminate  every  cause  which  can  introduce  into  his  determina- 
tions errors  depending  on  the  position  of  the  stars. 

The  possibility  of  emus  depending  on  the  right  ascension  of  the  stars  being  introduced  and 
perpetuated  has  been  pointed  out  by  different  astronomers,  and  especially  by  Mr.  Watford,  in  the 
monthly  notices  of  the  Royal  Astronomical  Society  for  October,  18(51.  The  existence  of  this  class 
of  errors  is  more  especially  to  be  feared,  because  under  the  system  of  reducing  observations  in 
right  ascension,  now  almost  universally  adopted,  they  will  tend  to  perpetuate  themselves  when 
once  introduced.  .Moi co\  IT,  owing  to  the  diurnal  and  annual  inequality  in  the  conditions  to  which 
the  observer  and  the  instrument  necessarily,  and  the  clock  generally,  are  subjected,  the  original 
introduction  of  the  class  of  errors  referred  to  is  very  easy.  A  mathematical  examination  of  the,  law, 
according  to  which  they  will  be  perpetuated,  may  not  be  uninteresting. 

In  the-  system  of  reduction  now  generally  adopted,  the  mean  of  all  the  clock  stars  observed  b\ 
one- observer  during  a  tour  of  duty  is  assumed  to  lie  free  from  error.  Whatever  error  this  mean 
maybe  affected  with,  the  same  error  will  affect  the  mean  of  the  concluded  positions.  The  alge- 
braic aggregate  of  the  errors  in  the  adopted  positions  will  be  distributed  among  the  concluded 
positions.  If  the  adopted  clock  rate'  be  correct,  this  distribution  will  be  a  uniform  one,  otherwise 
it  will  vary  with  the  position  of  the  star  in  the  group. 

Suppose,  now,  that  the  adopted  positions  are  affected  with  an  error  of  the  form  n  sin  <i  +  b  cos  n. 
Then,  throughout  one-half  the  circle  the  star  positions  will  be  systematically  too  small,  and  in  the 
other  half  systematically  too  great.  And  all  clock  errors  not  derived  equally  from  the  two  classes 
of  stars  will  be  erroneous,  and  the  error  will  thus  perpetuate  itself.  It  will,  indeed,  tend  to  grow 
a  litth'  smaller  with  each  revision  of  the-  clock  stars;  but  this  tendency  will  be  counteracted  by  the 
probable  erroneous  proper  motions,  and,  under  the  actual  circumstances  of  obsci A  at  ions,  will  be 
very  small.  If  we  examine  the  published  observations  we  shall  liiul  that  only  a  small  fraction  of 
the  stars  observed  are  distant  more  than  three  hours  from  the  mean  of  the  group  on  which  they 
depend,  nearly  all  the  stars  of  a  group  being  included  in  a  space  of  from  four  to  six  hours.  If  we 
suppose;  the  groups  to  be  of  a  uniform  length  of  six  hours,  and  to  be  equally  distributed  around  the 
circle,  the  right  ascension  of  any  one  star  will  depend  wholly  upon  the'  adopted  positions  of  stars 


6  POSITIONS   OF   FUNDAMENTAL    STARS. 

within  isix  hours  of  it,  and  the  stars  within  a  space  of  two  hours  on  each  side  will  have  more  weight 
in  fixing  its  position  than  all  the  others  combined,  the  weight  of  each  star,  or  the  number  of  times 
it  is  compared  with  the  star  in  question,  increasing  in  arithmetical  progression  as  we  approach  the 
latter.  In  algebraic  language,  the  number  of  comparisons  will  be  proportional  to  O1'  —  J«,  J  « 
being  the  difference  of  right  ascension.  If  we  represent  the  number  of  comparisons  with  any  one 
star  by  n,  and  the  error  of  the  adopted  position  of  this  star  by  y>,  the  error  of  the  concluded  posi- 
tion of  the  star  compared  will  be  represented  by 

~np 
Tw  ' 

To  change  the  terms  of  this  fraction  into  definite  integrals,  we  have  only  to  multiply  each  of 
them  by  da,  and  substitute  /  for  I.  The  fraction  thus  becomes 

fnp  da 
fn  d  a 

Put  «0  for  the  right  ascension  of  the  star,  the  error  of  whose  concluded  position  is  sought, 
and  a  for  the  right  ascension  of  any  star  with  which  it  is  compared.  Then,  on  the  above 
hypothesis,  we  have 

*=«||*d=(«-*o)}j 

the  sign  being  yo  taken  that  the  difference  ot  right  ascension  shall  always  be  negative.    The  factor 
c  depends  on  the  entire  number  of  observations,  and  may  be  supposed  equal  to  unity,  as  it  disap- 
pears from  the  fraction.     Substituting  this  value  of  n,  and  putting  c  for  the  final  error  in  the.  con 
eluded  position  of  the  star  resulting  from  the  errors  in  the  adopted  positions  of  the  clock  stars,  we 
have 


J*«  C" 

(i~ —  uo  "f"  ")j"' tt  "t~  I 
!*o  —  ^  " J«o 


7*"o  /'"c 

J«o  —  i  ~  "  •/•o 


The  value  of  the  denominator  of  this  fraction  is 

i*». 

Let  the  adopted  right  ascensions  of  the  clock  stars  now  be  affected  with  a  periodic  error 

«  sin  «  +  b  cos  «  +  a'  sin  '2  a  -f  b'  cos  2« 
Tut 

a  =    fe  cos  fi, 
b  =    fc  siii  ^9, 
ft'  =    k'  cos  ft', 
b'  =    k'  siii  ,5', 
x  =    a  +  ft, 
X'  =  2a  +  ft';' 
which  gives 

p  =  Tc  sin  x  +  k'  siii  x', 


The  substitution  of  these  values  reduces  the  numerator  of  c  to  the  form 


POSITIONS    OF    FI'NDAMKNTAI.    STAlis. 
The  value  of  tlio  tirsl  term  of  tliis  expression  is 

-t  sin  (a0  +  ,3); 
that  ol'  tin-  second 

(li--)Jtsiu(«0  +  ,;): 

th;it  of  tin-  third  vanishes,  ;uid  that  of  the  fourth  is 

/.-'  sin  (1>«C +  ,;')• 
The  \alue  ol'  r  therefore  lieconies 

1H-  sin  (« 


or,  writing  «  for  «0,  so  that  «  now  re])resents  the  right  ascension  of  any  star,  the  position  of  which 
is  determined  by  observation, 

S  I 

e  =  -^j-  (a  sin  a  +  ft  cos  «)  -f-     ,  (n1  sin  2a  +  ft'  cos  li«)  . 

It  appears,  then,  that  in  the  case  supposed,  that  in  which  the  groups  are  of  a  uniform  length 
of  six  hours,  and  the  clock  stars  are  scattered  uniformly  through  each  group,  each  revision  of  the 
fundamental  catalogue  will  tend  to  diminish  the  error  of  single  period  by  rather  less  than  one-ufth, 
and  that  of  double  period  by  more  than  one  half.  The  latter  will  therefore  be  cut  down  much  more 
rapidly  than  the  former. 

In  addition  to  this,  it  may  be  noted  that  errors  of  single,  period  are  those  most  likely  to  have 
found  entrance  into  the  original  catalogue,  arising,  as  they  do,  from  the  ett'ect  of  the  diurnal  change 
of  temperature  upon  the  instrument  and  the  clock.  It  is  also  to  be  remembered  that  this  same 
cause  may  perpetuate  the  errors  in  question.  It  is  true  that  the  effect  of  a  uniform  diurnal  change 
will  be  eliminated  from  a  symmetrical  year's  work.  But  the  diurnal  change  of  temperature  is  not 
uniform  throughout  the  year,  and  it  is  also  unsafe  to  assume  that  its  ett'ect  upon  the  clock  is  the 
same  in  all  seasons. 

This  same  uncertainty  will  att'eet  the  results  of  comparisons  of  single  stars  or  groups  of  stars. 
The  comparison  must  alwa\s  be  made  with  a  clock  rate  deduced  from  its  change  of  error  during  a 
period  of  at  least  twenty-four  hours,  while  the  interval  of  comparison  is  only  a  fraction  of  a  day, 
during  which  the  clock  rate  may  be  systematically  different  from  its  mean  rate  during  the  twenty- 
four  hours. 

In  arranging  the  transit  circle  observations  for  1800  and  1807,  the  following  arrangements 
were  planned  as  necessary  to  a  reliable  determination  of  the  possible  systematic  error  in  the  adopted 
right  ascensions  of  the  clock  stars  of  the  form  a  sin  «  +  /J  cos  «: 

1.  That  the  clock  should  be  placed  in  a  position  where  it  would  be  tree  from  all  diurnal  ine- 
quality of  temperature. 

'_'.  That  when  practicable  the  same  observer  should  observe  as  many  as  six  clock  stars  between 
-I'1  and  .'!''  of  the  day,  and  a  corresponding  group  between  O'1  and  l.V'  mean  time  of  the  night. 
Also,  that  similar  combinations  of  groups  twelve  hours  apart  should  be  made  in  the  morning  and 
evening  when  practicable.  The  systematic  errors  would  then  be  of  equal  magnitude,  and  of  oppo- 
site signs  in  each  pair  of  groups  compared.  K.s  continuing  the  observations  through  an  entire 
year  all  regular  diurnal  inequalities  arising  from  the  observer  or  the  instrument  would  be  elimi- 
nated. And,  by  using  the  instrument  in  opposite  positions  during  the  two  years,  all  diurnal  ine- 
qualities in  its  collimation,  whether  regular  or  irregular,  will  be  eliminated. 

Kate  of  the  clwJc. — During  the  year  18G(i  the  Kessels  clock  was  in  the  superintendent's  room, 
where  it  was  supposed  to  be  tree  from  all  appreciable  diurnal  inequality  of  temperature.  This  con- 
dition was  well  fulfilled,  except  during  the  summer  months,  when  it  was  found  that  the  night 
temperature,  as  indicated  by  a  pointer  on  the  pendulum  rod,  was  about  5°  lower  than  the  highest 
day  temperature.  As  such  a  change  might  be  deleterious,  the  clock  was,  in  February,  1807, 
removed  to  a  niche  in  the  base  of  the  great  pier  of  the  equatorial,  where  its  temperature  varies 
but  a  very  few  degrees  during  the  entire  year. 

Deeming  it  advisable  to  test  the  rate  of  the  clock  under  changes  of  temperature  as  severely  as 
possible,  it  was.  during  the  months  of  November  and  December,  ISOC-flj^aaed  to  changes  of 

it^S^s 

[VIXYl&SXTTl 


8 


POSITIONS    OF    FUNDAMENTAL    STARS. 


temperature  several  times  more  wide  and  rapid  than  any  it  had  met  with  in  actual  use,  while  its 
changes  of  rate  were  determined  by  comparison  with  the  standard  mean  time  clock  in  the  chro- 
nometer room,  which  had  about  as  even  a  rate;  as  the  Kessels  clock.  The  changes  of  temperature 
were  effected  by  closing  the  door  of  the  room,  opening  the  windows,  and  cutting  oil'  the  heat 
for  periods  of  one  day  or  more  during  exceptionally  cold  weather,  and  reversing  the  process  when 
the  temperature  nearly  ceased  to  fall.  The  clock  comparisons  wew  made  at  irregular  intervals. 
The  results  are  presented  in  the  following  table,  which  gives : 

The  mean  dates  and  sidereal  times  of  coincidence  of  beats  of  clocks. 

The  sidereal  interval  following  each  comparison. 

The  reduction  of  this  interval  to  solar  time. 

The  length  of  the  sums  of  one  or  more  of  these  intervals  in  hours. 

The  relative  loss  of  the  Kessels  (sidereal)  clock  during  these  intervals. 

The  resulting  daily  losing  relative  rate  of  the  sidereal  clock. 

The  mean  reading  of  the  temperature  pointer  during  the  rate-interval.  Each  unit  of  r  corre- 
sponds to  about  .'5°  Fahrenheit. 


Menu  date. 

Sidereal 
time  of  coin- 
cidence. 

Sidereal 
intervals. 

Reduction  to 
solar  time. 

Intervals 
of  time. 

Relative 
lossol'sid. 
clock. 

Relative 

daily  rate 

T 

1866. 

/I.         Ml.       ••». 

/I.        Ml.       8. 

X. 

/i. 

•V. 

K. 

Nov.           25.  9 

13     43    33 

8      8    15 

79.  988 

8.1 

.012 

—      .  030 

+     3.2 

26 

21     51     48 

ii    30    38 

6.002 

22    28    26 

334 

29.991 

3.7 

—        .(MIT 

.047 

+     1.8 

1    31     30 

3    58     46 

39.  117 

5    30    1C 

2    49    44 

27.807 

6.8 

—       .076   —       .268 

1.4 

8    20       0 
12    36     13 

4     16     13 

1     49     50 

41.974 
17.994 

4.3 

—      .026 

—      .144 

-    3.4 

14    26      3 

289 

20.  995 

4.0 

.011 

—      .066 

—     1.9 

27 

16     34     12 

2    44     51 

27.  006 

2.7 

+      .006 

+      .053 

+     1.0 

19     19      3 

3    52      7 

38.027 

3.9 

+       .027 

+      .106 

+     1.8 

23    11     10 

Dco.             2.  9 

13    47     41 

3    27     27 

33.  986 

3.4 

.014 

.  1)1)8 

—     0.3 

3 

17     15       8 

2    32     32 

24.  989 

2.5 

.011 

.108 

—    0.5 

19    47     40 

6    24     25 

62.  977 

6.4 

—       .023 

—      .088 

+     1.3 

2     12      5 

22     17     27 

219.  109 

22.3 

+      .109 

+       .  115 

+     2.5 

4 

0    29     32 

13     5fl     45 

137.  082 

13.9 

+      .082 

+       .142 

+     2.8 

14     26     17 

10     28     55 

162.010 

16.5 

+      .inn 

+       .015 

+     3.5 

5 

6     55     12 

. 

11 

22    54     48 

16     52     28 

165.  868 

16.9 

.132 

.187 

-    4.4 

15     47     16 

7     37     42 

74.  983 

7.6 

.017 

.  054 

—    8.3 

12 

23    24     58 

15     15     14 

149.939 

15.3 

.  081 

.096 

—    9.  5 

14     40     12 

II     51     :,5 

8.996 

15     35      7 

4     28    28 

13.  981 

5.4 

.023 

.1(15   —     0.2 

18 

20      3     35 

3     51     58 

:!8.  003 

3.9 

+      .003 

+       .  018  j-  •     1.  3 

23    55    33 

15     34     25 

33.061 

15.  6 

+       .081 

+       .  124           0.  0 

15    29    58 

4     59     18 

49.  033 

5.0 

+       .  033 

+       .159   +0.8 

14 

20    2!)     l(i 

3    27     28 

33.  988 

3.  5 

.012 

.082 

23    56     44 
15     12    21 

15     15     37 
3    27     31 

150.  002 
33.  997 

15.  3 
3.  5 

+       .002 
—       .003 

+       .003   --     5.5 
.  021 

15 

18     39    52 

POSITIONS    OK    KfNDAMKNTAL    STARS.  9 

The  probable  result  of  these  comparisons  is  that  the  losing  daily  rate  of  the  clock  increases 
by  Os.()4  for  each  unit  of  increase  in  r.  or  by  Os.0i:$  for  each  rise  of  1°  in  flic  temperature.  If  we 
suppose  a  periodic  diurnal  change  of  (5°  in  the  temperature,  or  3°  on  eacli  side  of  the  mean,  the 
resulting  inequality  in  the  clock  rate  will  be 


ilt 

<•  being  the  inequality  of  clock  correction,  and  the  unit  of  t  being  one  day.     Integrating,  we  have 
for  the  resulting  inequality  in  the  clock  error,  and  in  the  reduced  right  ascensions  of  stars, 


cos 


=  Oa.OOG  cos 


The  discordance  of  the  results  is  such  as  to  leave  the  magnitude  of  this  small  correction 
doubtful.  The  rates  were  therefore  compared  with  the  actual  recorded  changes  of  temperature 
during  the  summer  of  ISiiii,*  and  the  result  was  that  the  effect  of  change  of  temperature  was  not 
nearly  so  great  as  this,  and  was,  indeed,  in  the  opposite  direction.  The  temperatures  and  rates 
are  compared  in  the  following  table: 


Limiting  ilatrs. 

Mran  rates 
bet.  (lairs. 

Mean  tem- 
peratures. 

d.        h. 

8. 

o 

l-(*i.  May  23      12.4 

+        0.25 

64.6 

25        5.5 

+        0.07 

70.5 

28      10.6 

+        0.14 

65.6 

31      11.0 

+        0.09 

71.0 

June     4       I  Mi 

+        0.04 

74.  5 

18       14.  0 

+        0.06 

6!».  '.' 

20       12.  6 

+        0.  12 

72.0 

21'      12.0 

+        0.14 

75.8 

23       10.  4 

+        0.  12 

81.6 

26.9    5.7 

+        0.00 

75.  1 

28.  9    4.  8 

+        0.13 

72.1 

July    3      11.6 

+        0.11 

80.2 

8.9    5.1 

+        0.00 

76.6 

13      15.  1 

+        0.01 

84.  H 

19       11.4 

Taking  the  differences  of  the  successive  numbers  in  the  columns  of  rate  and  temperature,  we 
have  a  series  of  changes  of  rates  corresponding  to  changes  of  temperature.  If  we  change  the 
signs  of  the  corresponding  pairs  in  which  the  temperature  change  is  negative,  and  then  take  the 
sum  of  each  series,  we  find 

Sum  of  changes  of  temperature 60° 

Sum  of  changes  of  rate —  0.R26 

The  daily  rate,  therefore,  appears  to  diminish  by  Os.004  for  each  rise  of  1°  in  the  temperature. 

The  apparent  difference  between  the  e fleet  of  natural  and  artificial  changes  of  temperature 
may  be  due  to  the  greater  rapidity  of  the  latter.  In  a  rigorous  investigation  the  rate  ought  to  IM> 
supposed  to  depend  upon  the  rate  of  change  of  the  temperature,  as  well  as  the  absolute  amount  of 
the  latter.  In  a  mercurial  pendulum  such  an  effect  would  be  likely  to  arise  from  the  different 
degrees  of  rapidity  with  which  the  mercury  and  the  rod  would  answer  to  changes  of  temperature. 
The  experiments  just  detailed  seem,  however,  to  show  that  ill  the  Kessels  clock  the  effect  is  very 
small,  if  not  altogether  insensible — a  result  not  improbable  in  the  case  of  a  gridiron  pendulum. 

found  in  Washington  Observations  for  IHIiti,  Introduction,  pp.  xx.xix  ami  xl. 


10  POSITIONS    OF   FUNDAMENTAL    STARS. 

I  conclude  that  the  effect  of  the  diurnal  change  of  temperature  to  'which  the  clock  was  actually 
exposed  may  be  safely  pronounced  insensible. 

Effect  of  the  barometric  pressure  on  the  clock. — During  the  month  ending  February  7,  18C7,  the 
barometer  was  subject  to  unusually  wide,  and  rapid  fluctuations.  The  comparison  with  the  clock 
rates  indicated  an  increase  of  Os.27  in  the  daily  losing  rate  for  every  inch  in  the  rise  of  the  barome- 
ter. This  correction  has  not  been  employed,  as  it  can  give  rise  to  no  systematic  diurnal  inequality. 

Effect  of  the  galvanic  current. — An  opinion  has  prevailed  that  the  passage  of  the  galvanic  cur- 
rent through  the  pendulum  might  affect  the  clock  rate.  This  was  tested  by  throwing  the  current 
on  and  off  during  alternate  intervals  of  from  4Jto  13  hours,  and  comparing  with  the  mean-time  clock 
at  each  change.  The  result  was 

8. 

With  battery  on  the  mean  relative  hourly  rate  was 0.038 

With  battery  off  it  was 0.040 

Not  knowing  any  way  in  which  the  current  could  appreciably  influence  the  motion  of  the  pen- 
dulum, I  regard  this  difference  as  accidental. 

Irregularities  of  clock  rate. — During  several  months  from  April,  1867,  observations  were  made 
with  great  regularity.  This  period  was  divided  into  intervals  of  as  near  ten  days  each  as  practica- 
ble, the  dividing  points  being  epochs  of  determination  of  clock  error.  The  errors  "thus  arbitrarily 
selected  were  interpolated  to  the  times  of  such  intermediate  determinations  as  were  three  days  or 
more  distant  from  each  end  of  the  period,  and  compared  with  these  determinations.  The  mean  dis- 
cordance was  Os.12.  It  appears,  then,  that  if  the  clock  error  were  determined  but  once  in  ten  days, 
the  intermediate  errors  would  average  about  OM2  during  the  period  in  question.  But  I  think  that 
during  this  period  the  rate  was  more  regular  than  the  average  one,  and  that  the  mean  result  for  the 
two  years  would  be  from  08.1(5  to  OM8. 

As  the  clock  corrections  are  published  in  full  in  the  introduction  to  each  volume  of  observa- 
tions, it  seems  unnecessary  to  repeat  the  data  on  which  these  results  are  founded. 

A  diurnal  change  in  the  pointing  of  the  instrument  will  have  the  same  effect  as  one  in  the  clock 

rate.     The  collimation  error  is  known  to  undergo  a  change  of  08.003  for  every  change  of  1°  Falnvn- 

.heit  in  the  temperature.     A  regular  diurnal  change  in  the  pointing  of  the  instrument  may,  therefore, 

be  inferred.     Its  effect  will,  however,  be  eliminated  from  the  mean  of  the  results  of  the  two  years 

by  the  reversal  of  the  instrument. 

There  are  few  results  for  diurnal  change  of  level,  it  being  considered  very  improbable  that  there 
should  be  such  a  change.  These  few  do  not  indicate  such  a  change. 

A  diurnal  change  of  azimuth  can  be  most  certainly  detected  from  the  observed  transits  of 
Polaris.  Its  discussion  is,  therefore,  deferred  for  a  subsequent  section. 

Having  considered  the  sources  of  diurnal  inequality,  the  possibility  of  which  may  be  seen  a 
priori,  we  now  proceed  to  the  discussion  of  the  observations  of  stars.  The  method  of  discussion  is 
founded  on  the  consideration  that  there  may  be  a  systematic  difference  between  the  clock  correc- 
tions determined  at  different  times  of  the  day.  Such  a  difference  would  result  from  a  regular  diur- 
nal change  either  in  the  clock,  the  instrument,  or  the  personal  equation  of  the  observer.  However 
improbable  its  existence  may  seem,  the  question  of  its  reality  is  to  be  finally  settled  by  the  observa- 
tions themselves.  Let  us,  then,  consider  the  transits  of  two  groups  of  stars  several  hours  apart. 
We  compare  the  observed  sidereal  interval  between  the  transits  with  the  computed  difference  of 
right  ascensions.  The  clock  rate  being  supposed  accurately  known,  the  difference  between  the 
observed  and  computed  intervals  may  be  due  to  systematic  error  in  the  right  ascensions  of  the  two 
groups  of  stars,  and  to  changes  in  the  observer  or  instrument.  The  first  source  of  error  will  be  con- 
sidered to  depend  on  the  right  ascension,  and  to  be  of  the  form  a  sin  All  +  !>  cos  All;  the  second 
will  be  supposed  to  depend  on  the  hour  of  the  solar  day.  In  any  one  day  it  will  be  impossible  to 
distinguish  between  the  effects  of  these  two  causes.  Hut,  in  the  course  of  a  year,  the  first  cause  will 
undergo  ;>(!(•  changes  while  the  second  will  undergo  305,  and  the  effects  may,  therefore,  be  completely 
separated. 

Since  the  second  cause  may  not  change  regularly  in  the  course  of  the  day,  the  latter  will  be 


1'OSITIONS    OF    l<'rM>AMKNTAI.    STAKS.  1  1 

divided  into  six  parts,  in  each  of  wliicli  the  second  elfeet  will  have  separate  and  independent  values. 
The  ilala  have,  therefore,  been  divided  into  three  classes,  as  follows: 

1.  Comparisons  of  groups  of  stars  observed  in  the  forenoon,  with  corresponding  groups  observed 
by  the  same  observer  during  the  evening  following;'. 

"2.  Similar  comparisons  in  which  the  first  group  was  observed  in  the  afternoon,  and  the  second 
near  or  soon  after  midnight. 

;{.  Similar  comparisons  in  which  the  lirst  group  was  observed  in  the  early  evening,  and  the  sec- 
ond in  the  early  morning.  . 

Each  difference  between  the  observed  and  computed  intervals  of  a  pair  of  groups  gives  an  equa- 
tion of  the  form 

d  =  a  +  ma-\-nb, 

where 

J,  excess  of  computed  over  observed  interval. 

«,  amount  by  which  the  lirst  group  is  systematically  observed  too  late,  as  compared  with  the  sec- 
ond, or  the  amount  by  which  the  observed  interval  is  systematically  too  small. 
M,n,  differences  between  the  mean  values  of  sin  a  and  cos  «  for  the  two  groups. 

The  data  for  the  separate  comparisons  are  given  in  the  following  table,  which  shows 

(1.)  The  date,  the  day  beginning  with  the  tour  of  duty  of  the  observer. 

(li.)  The  initial  of  the  observer.  • 

(3.)  The  sidereal  hour  corresponding  to  the  mean  of  the  first  group  of  stars. 

(4.)  The  number  of  stars  in  the  group. 

(.">.)  The  mean  correction  in  hnndredths  of  seconds  to  the  computed  right  ascensions  of  tl;e  stars 
of  the  group.  In  the  year  1866  these  computed  positions  are  taken  from  the  American  Ephemeris, 
without  correction,  and  the  mean  given  is  simply  that  of  the  "  miscellaneous  corrections"  in  the  last 
column  of  the  printed  observations.  In  1867  the  corrections  refer  to  the  adopted  positions,  and  are 
the  mean  excesses  of  the  "adopted"  over  the  "apparent"  clock  correction. 

(6,)  (7,)  (8.)  The  corresponding  quantities  for  the  opposite  group  of  stars. 

(9.)  The  values  of  J,  or  the  excess  of  the  computed  over  the  observed  difference  of  right  ascen- 
sion of  the  groups.  A  is  the  difference  between  columns  (5)  and  (8),  corrected  for  the  change  in  the 
collimation  of  the  instrument  due  to  the  change  of  temperature  between  the  times  of  observation. 

J  forms  one  side  of  the  equation  of  condition  of  the  form  already  given,  only  that  in  compari- 
sons of  the  second  and  third  classes  «  is  replaced  by  /Sand  y  respectively. 

In  columns  (5,)  (8,)  and  (9)  the  units  represent  huudredths  of  seconds  of  time. 


12 


POSITIONS    OK    FUNDAMENTAL    STARS. 


Date. 

Obs. 

Hour. 

No.of 
stars. 

Mean 
correc'i). 

Hoar. 

No.of 

stars. 

Mean 

ronvc'n. 

Equation  of  condition. 

1866. 

January      9 

R. 

1.9 

2 

+      6 

14.1 

2 

+       4 

+     3  =  :  7     +     1.0  a     +     1.  6  ft 

H 

H. 

21.0 

3 

1 

6.8 

4 

—      2 

+     3  =  0    -  •     1.  5        +     0.  9 

31 

N. 

19.1 

3 

+      3 

7.0 

3 

y 

+  ll  =  a    -        1.7        +     0.6 

31 

N 

-22.1 

3 

—      7, 

10.6 

3 

+       5 

-  11  =  /3    -  -    0.  9        +1.5 

February     1 

R. 

19.1 

2 

+      5 

7.0 

3 

0 

+     6  =  0    -  -     1.7        +0.6 

1 

R. 

23.9 

3 

1 

11.3 

3 

+      3 

-    8  =  0    -  -    0.9        +1-7 

2 

H. 

22.8 

2 

—      2 

12.0 

4 

—      3 

+     3  =  0    —    0.  3        +1.7 

8 

T. 

0.0 

3 

+       3 

12.  9 

3 

1 

+     6  =  y     +     0.3        +1.8 

6 

H. 

18.9 

5 

+    r, 

•  5.9 

6 

4 

+  10  =  a    -  •     1.7         +0.3 

6 

H. 

0.8 

5 

-'  2 

14.0 

•    3 

—      3 

+     3  =  7     +     0.7        +     1.5 

16 

H. 

18.3 

.    4 

+      1 

5.9 

3 

—      3 

+     5  =  a    -  •     1.8                0.  0 

1(> 

H. 

1.3 

3 

—            1 

11.4 

5 

+      2 

-2  =  y    +     0.2        +1.7 

17 

T. 

20.8 

3 

+       4 

9.5 

2 

—      8 

+  13  =  a     -        1.  3        +     1.3 

20 

R. 

1.0 

4 

+      4 

12.4 

3 

—      2 

+     8  =  0     +     0.4        +     1.7 

21 

T. 

20.  7 

2 

+       6 

10.0 

3 

—      6 

+  13  =  a    -  •    1.2        +1.3 

26 

H. 

18.6 

3 

+      3 

7.2 

4 

—      4 

+     8  =  a   .—     1.7        +     0.5 

March          5 

H. 

1.9 

2 

+   10 

13.0 

6 

—      3 

+  15  =  ;?    +    0.8        +1.6 

5 

H. 

6.6 

3 

—      6 

18.1 

2 

+       4 

-  10  =  y     +     1.  8            -     0.  2 

8 

N. 

23.2 

4 

0 

11.3 

5 

—      2 

+     3  =  0    --    0.  4        +1.7 

8 

N. 

6.8 

2 

—      6 

17.9 

3 

+     H 

-17  =  y     +     1.7           -    0.2 

10 

T. 

0.2 

3 

+       4 

11.7 

5 

1 

+     6  =  0            0.0        +1.8 

14 

N. 

21.4 

2 

—      3 

10.7 

4 

—      6 

+    4  =  o    -  •    1.0        +1.5 

16 

H. 

6.1 

2 

+       6 

18.0 

4 

—      2 

+     8  =  7    +     1.8                0.0 

22 

R. 

23.8 

2 

+       4 

11.9 

4 

—      6 

+  11  =a     —     0.  1        +1.9 

26 

N. 

1.3 

3 

+       3 

13.0 

3 

+      3 

+    2  =  0     +     0.7        +     1.6 

27 

R. 

22.3 

2 

—      9 

10.5 

3 

+      2 

—  10  =  a    —    0.  8        +1.5 

30 

N. 

22.1 

3 

+      4 

11.3 

3 

—      7 

+  12  =  o    -  -    0.  7        +1.5 

April          26 

R. 

0.3 

2 

+      4 

14.0 

2 

—      4 

+     9  =  a     +     0.  6        +     1.  5 

27 

H. 

5.0 

^     3 

—      5 

13.5 

3 

+      2 

-5  =  0     +     1.2        +1.1 

May             4 

H. 

0.3 

2 

4 

13.0 

4 

+      2 

-    5  =  a     +     0.  4        +1.7 

12 

T. 

5.2 

4 

+      1 

15.4 

4 

+      1 

+     2  =  0     +     1.5        +0.8 

14 

N. 

5.4 

3 

+      2 

16.0 

4 

+       3 

+     1=0     +     1.6        +     0.7 

15 

R. 

5.2 

2 

—      2 

16.1 

4 

+      3 

-3  =  0     +     1.6        +0.7 

22 

H. 

1.3 

2 

+       8 

12.8 

5 

—      5 

+  14  =  n    +     0.  6        +1.6 

22 

H. 

5.4 

3 

+     o 

17.6 

4 

—      1 

+     4  =  0+1.7        +0.3 

83 

T. 

0.6 

3 

+      5 

12.6 

2 

—      1 

+     7  =  a     +     0.  5        +1.7 

24 

N. 

1.9 

2 

0 

15.1 

3 

^ 

+     2  =  0     +     0.9        +1.5 

24 

N. 

5.5 

3 

0 

18.1 

3 

+      2 

+     1=0     +     1.8        +0.1 

25 

H. 

1.1 

4 

+    1 

14.4 

2 

0 

+     2  =  a     +     0.9        +1.5 

28 

N. 

6.0 

6 

1 

15.  8 

5 

+      2 

0  =  0     +     1.6        +0.5 

30 

T. 

1.9 

2 

—      3 

13.8 

2 

0 

—     l  =  a     +     0.9        +1.5 

30 

T. 

7.4 

2 

—     14 

17.1 

3 

+     12 

—  23  =  0     +     1.  6           -    0.  1 

June             4 

N. 

7.0 

3 

—      7 

16.3 

3 

+       4 

-8  =  0    +     1.6        +0.1 

8 

R. 

6.9 

3 

—      2 

17.8 

3 

+     .7 

—    6  =  0     +     1.8           -    0.2 

11 

N. 

7.5 

3 

—      5 

18.6 

3 

+      2 

-4  =  0     +     1.8           -    0.6 

12 

R, 

3.7 

2 

n 

15.0 

2 

3 

+     5  =  a     +     1.4        +1.2 

16 

T. 

3.6 

2 

0 

15.6 

3 

+       4 

-2  =  o     +     1.5        +1.2 

18 

N. 

7.6 

2 

—      6 

18.  5 

4 

+       3 

-6  =  0     +     1.8           -    0.5 

22 

R. 

6.2 

4 

4 

18.0 

3 

+       1 

—    8  =  0     +     1.9           -    0.1 

( 

I'OSITIONS    OK    FUNDAMENTAL    STA 


13 


Hair. 

01. 

Hour. 

No.  of 

stars. 

Mean 

i  mi  i  i-'n. 

Hour. 

No.of 

stars. 

Mean 
convc'ii. 

Equation  of  condition. 

L866. 

.lunc            23 

11. 

7.6 

2 

4 

15.8 

I 

+      6 

-    7  =  0     +     1.6  a     +     0.  Ib 

25 

N. 

6.  II 

2 

-     10 

18.5 

3 

+      5 

-12  =  a     +     1.9        —    0.2 

26 

R. 

4.8 

2 

4 

16.4 

4 

4       3 

-5  =  0     +     1.7        +0.8 

n 

II. 

14.3 

2 

4 

1.7 

S 

+      5 

-9  =  7    —    0.8        —    1.7 

July              2 

N. 

4.8 

2 

+      2 

17.4 

4 

+      5 

•1  =  0    +    1.8        +0.5 

2 

N. 

13.4 

2 

—      !l 

1.9 

2 

4-      2 

—  11  =  7    -  -    0.9        —    1.7 

5 

N. 

5.2 

2 

—      6 

If..  7 

4 

+      1 

-5  =  a    +     1.8        +0.5 

5 

N. 

11.6 

2 

—      6 

1.6 

2 

+      8 

—  11  =  7    —    0.3        —    1.7 

6 

K. 

4.8 

2 

4 

16.7 

3 

+      3 

-5  =  o    +     1.8        +0.7 

6 

K. 

14.0 

2 

—      4 

1.6 

2 

+       4 

-    8  =  7    -  -    0.9           -1.7 

7 

11. 

13.4 

2 

—       1 

2.4 

2 

+      3 

•    4  =  y    -  -    1.0               1.6 

11 

T. 

5.1 

3 

0 

16.8 

4 

+      2 

.    l  =  a'   +     1.8        +0.6 

11 

T. 

i-.'.  i; 

3 

—      9 

21.1 

2 

+     10 

-  16  =  7    +    0.  1           -1.8 

111 

H. 

5.2 

4 

4 

17.2 

5 

4-     4 

-7  =  0    +     1.8        +0.5 

a 

H. 

;i.  f, 

2 

-     14 

r.t.  :, 

4 

4-     7 

-18  =  0     +     1.4        —    0.1 

13 

II. 

13.7 

3 

—      5 

1.7 

2 

4-      3 

-    8  =  7    -  -    0.9           -1.7 

14 

T. 

5.4 

4 

4 

17.3 

4 

+     2 

•4  =  0    +    1.8        +0.5 

14 

T. 

I-'..', 

3 

0 

0.5 

3 

—      4 

+    7  =  7    •  -    0.3            -1.8 

16 

N. 

f>.  5 

3 

-       5 

18.0 

4 

4-      3 

-    6  =  0    +     1.8        +    0.2 

19 

K. 

5.3 

3 

—      3 

17.5 

3 

4-      2 

-3  =  o    +     1.8        +0.3 

23 

N. 

13.6 

2 

—      4 

1.9 

2 

0 

-    2  =  7    •  -    0.  9           -1.7 

26 

N. 

6.2 

2 

4 

18.4 

5 

+      4 

-    6  =  0    +     1.8          -    0.2 

26 

N. 

11.5 

4 

—      2 

1.1 

2 

0 

+    1  =  0    -  -    0.  2           -1.8 

27 

H. 

11.5 

3 

—      6 

20.9 

3 

4      5 

-8  =  0    +    0.8        —    1.5 

31 

H. 

f..  2 

5 

—       1 

18.9 

4 

4-      4 

-3  =  o    +     1.8        —    0.4 

August        3 

T. 

6.6 

3 

—      5 

18.4 

3 

+      8 

-ll  =  o    +     1.8        —    0.3 

3 

T. 

12.5 

2 

—      1 

23.0 

2 

—      6 

+    8  =  7    +    0.2           -1.8 

I 

N.. 

7.0 

3 

—  *  3 

19.4 

4 

+       2 

-    3  =  o    +    1.7       —    0.7 

10 

H. 

7.2 

3 

—      7 

19.3 

5 

4-      8 

—  13  =  a    +     1.  8        —    0.  7 

10 

11. 

12.0 

3 

—      7 

1.1 

2 

4 

0  =  0    -  -    0.  3        —    1.8 

15 

T. 

13.6 

2 

—      4 

0.2 

2 

4 

+    3  =  7    •  -    0.4           -1.8 

16 

R. 

7.5 

3 

—      5 

19.8 

4 

+      2 

—    5  =  0    +     1.7        —    0.9 

16 

R. 

II.  n 

2 

—    11 

23.2 

3 

4-      5 

-  13  =  7    •  -    0.  3        —    1.  7 

17 

II. 

7.2 

5 

—      1 

19.  » 

P 

4      2 

l  =  o     +     1.7        —     1.8 

17 

H. 

12.5 

3 

—      3 

22.6 

4 

+      3 

-    3  =  0    +    0.2           •    1.7 

18 

T. 

7.3 

3 

—      8 

19.2 

3 

+     13 

-20  =  o    +    l.  8        —    0.7 

20 

N. 

7.6 

4 

—      7 

21.2 

4 

+      6 

-12  =  o    +     1.6        —      .1 

20 

N. 

11.4 

2 

—      5 

0.8 

2 

+      5 

-    7  =  0            0.0        —      .8 

22 

T. 

7.6 

2 

—      9 

21.2 

2 

+      6 

-13  =  a+1.5        —       .1 

S..|,i,.|,il.cr  5 

T. 

13.6 

2 

4 

23.6 

2 

4 

+     3  =  0    --     0.3        —       .7 

8 

T. 

9.5 

2 

—     14 

21.1 

4 

+      5 

-18  =  a     +     1.3        —       .4 

8 

T. 

13.1 

2 

—      7 

0.4 

2 

4      3 

—    7  =  0    —    0.5        —      .8 

12 

T. 

0.8 

2 

•     11 

21.0 

3 

4-      9 

-18  =  a    +    1.2           -      .5 

13 

R, 

'.'.  6 

2 

0 

21.2 

4 

1 

+    3  =  a    +    1.2        —      .5 

14 

T. 

14.4 

2 

12 

23.8 

2 

4      2 

-  11=0    -  -    0.5        —       .7 

15 

R. 

13.8 

2 

7 

23.  0 

3 

+      3 

-    7  =  0    —    0.2           •      .7 

22 

N. 

12.4 

3 

-       5 

22.3 

4' 

4      6 

—    8  =  0    +    0.3        —      .8 

27 

28 

N. 
R. 

9.8 
12.1 

3 
2" 

1 
—    12 

23.0 
23.5 

3 
4 

+       7     ,    -    6  =  0     +     0.8        —       .6 
+      6       -  16  =  o     +     0.  1        —       .ft 

14 


POSITIONS    OF    FUNDAMENTAL    STARS. 


r 

Date. 

Obs. 

Hour. 

No.of 

btars. 

Mean 
orrec'n. 

Hour. 

No.of 
tars. 

Mean 
orrec'u. 

Equation  of  condition. 

1866. 

October        3 

H. 

10.4 

3 

4 

22.3 

4 

+      8 

—  11  =  o     +     0.8a     -  •     1.7  6 

4 

R. 

15.6 

2 

—      4 

0.2 

2 

+       8 

-    9  =  /3    -  -    0.  8           -1.5 

5 

H. 

10.4 

3 

—      7 

21.8 

4 

+      2 

—    7  =  0     +     0.9        —     1.6 

5 

H. 

14.4 

2 

—      3 

0.8 

2 

1 

+     l  =  l)    +    0.8           -1.6 

6 

N. 

11.0 

3 

1 

22.7 

2 

+       4 

—    3  =  a     +     0.  7        —     1.  8 

8 

N. 

12.3 

3 

4 

0.5 

4 

+      2 

—    4  =  a    -  -    0.  2           -     1.  8 

8 

N. 

15.1 

3 

—       1 

1.9 

2 

+      1 

0  =  ,i    -  •     1.2           -    1.5 

17 

H. 

11.4 

2 

—      3 

0.3 

3 

+      6 

—    8  =  a     +     0.  1           -.1.8 

17 

H. 

17.1 

4 

—      3 

6.2 

3 

1 

+     1  =  7    •  -     1.  8           -    0.  2 

18 

R. 

15.6 

2 

+      6 

4.4 

3 

—       6 

+  14  =  f)    -  -     1.  6        —  .  1.  0 

19 

H. 

17.7 

4 

—      2 

5.1 

3 

+      2 

—     1  =  y    -  -    1.  8           -    0.  4 

20 

N. 

-14.1 

3 

+      3 

0.1 

4 

+       3 

+     2  =  /J    --    0.5            -1.7 

25 

R. 

13.6 

2 

—      6 

1.4 

3 

+       1 

—    5  =  a    —    0.  8        —     1.7 

31 

H. 

11.0 

5 

4 

22.9 

4 

0 

—    3  =  a     +     0.5            -1.8 

November  2 

H. 

12.2 

2 

-    11 

1.3 

3 

+      5 

-  14  =  a    -  -    0.  5        —1.8 

2 

H. 

16.6 

4 

0 

4.8 

3 

+       4 

—     1  =  p    -  -     1.  7           -    0.  7 

5 

N. 

12.8 

2 

+       4 

1.9 

2 

—      2 

+     7  =  o    -  -    0.7            -1.7 

7 

T. 

12.9 

2 

—      4 

2.5 

3 

+      9 

—  12  =  a    —    0.  9           -1.7 

7 
8 

12 

T. 

N. 

N. 

17.3 
13.5 

17.7 

2 
3 
3 

-      6 

0 

+   10 

4.8 
2.5 
5.0 

2 

2 
4 

+      1 
+      8 
+      2 

—    5  =  f)    -  -    1.  8           -    0.  5 
-    7  =a    -  -     1.0           -1.6 
+  10  =  /3    -  -    1.  8           -     0.  4 

13 

R. 

13.8 

2 

+      2 

1.2 

2 

+      2 

+     l  =  a    --    0.8           -     1.7 

17 

T. 

13.8 

2 

—      5 

3.3 

2 

+      7 

-  ll  =  o    -  •     1.2           -    1.5 

20 

R. 

13.8 

2 

—      5 

1.9 

3 

—      4 

+     0  =  a    -  -    0.  9                1.7 

/           21 

T. 

13.5 

4 

+      5 

2.7 

3 

—      6 

+  ll  =  a    —     1.0        —     1.5 

26 

T. 

14.8 

3 

+      3 

1.5 

3 

+      3 

+     1  =  0    —     1.0        —     1.6 

26 

T. 

18.3 

3 

+      2 

8.0 

4 

—      3 

+    7  =  /3    -  -    1.7        +0.6 

December    4 

R. 

19.2 

2 

—      4 

6.5 

5 

+      2 

—    4  =  /3    —    1.8        +0.  4 

5 

N. 

14.6 

2 

+      3 

3.3 

3 

—      4 

+    7  =  o    -  -    1.3           -     1.4 

5 

N. 

19.2 

4 

+      6 

7.4 

3 

—      2 

+  10  =  /3    —    1.  7        +     0.  7 

10 

R. 

17.0 

2 

—      2 

3.2 

2 

—      3 

+    3  =  a    —    1.6       —    1.0 

12 

R. 

19.1 

2 

—      2 

6.6 

4 

+      2 

-    2  =  /3    -  -    1.8        +0.5 

20 

T. 

16.2 

3 

+      5 

2.8 

4 

—      8 

+  14  =  a    -  -    1.5           -     1.1 

20 

T. 

19.4 

4 

+      8 

7.0 

2 

—    10 

+  20  =  /3    --    1.8        +    0.7 

POSITIONS   OF    FUNDAMENTAL,   STARS. 


If) 


Hate. 

ni,*. 

Hour. 

No.,,1 
stars. 

Mean 

•OITCC'II. 

Hour. 

No.of 

St.  'IIS. 

Mean 
•OITCC'II. 

Initiation  of  condition. 

1887. 

January     l.r> 

H. 

22.  3 

2 

J 

7.8 

2 

1 

-    2  =  0    -  -    1.3  a     +     1.36 

18 

11. 

17.9 

3 

+         1 

5.6 

4 

0 

0  =  o    -  -    1.8        —    0.2 

19 

T. 

Ukl 

8 

0 

6.5 

2 

+      5 

-    6  =  0    -  •    1.8        +0.5 

22 

H. 

22.3 

2 

4 

CM 

2 

+      2 

-    8  =  0    -  -    0.4        +1.7 

23 

T. 

1-." 

2 

+       5 

6.9 

3 

4> 

+    6  =  0    •  •    1.9        +0.3 

23 

T. 

1.5 

2 

+      2 

11.7 

3 

—      2 

+     3  =  7     +     0.3        +1.8 

24 

N. 

17.6 

4 

—      2 

7.5 

2 

+      6 

-    9  =  o    -  •    1.8        +0.3 

24 

N. 

22.1 

2 

+      7 

10.7 

4 

4 

+    9  =  0    -  -    0.8        +1.7 

28 

N. 

1-.  1 

3 

+       4 

5.4 

3 

—      2 

+    5  =  0    —    1.9        —    0.1 

.".I 

H. 

18.6 

2 

—      6 

6.5 

2 

+       4 

-  11  =  o    -  -    2.0        +0.2 

29 

H. 

3.2 

2 

+      5 

15.1 

2 

0 

+    3=x    +     1.5        +     1.3 

Kcliniary     1 

H. 

19.1 

2 

—      6 

6.3 

3 

+      4 

-  11  =o    -  •    1.8        +0.4 

5 

II. 

3.5 

3 

1 

13.6 

2 

+      7 

-9  =  y    +     1.2        +1.4 

6 

T. 

19.1 

3 

1 

7.2 

2 

3 

+     l=a    -  •     1.8        +     0.  7 

6 

T. 

0.4 

2 

—      8 

12.4 

4 

+      5 

-  14  =  y    +     0.  1        +1.8 

7 

N. 

19.7 

2 

4 

7.4 

2 

+      2 

-7  =  a    —    1.8        +0.  8 

7 

N. 

22.8 

2 

—      2 

9.5 

2 

+      4 

-    8  =  0    -  -    0.9        +1.7 

11 

N. 

23.5 

2 

+      2 

9.3 

3 

+      2 

-    2  =  0    —    0.8        +1.6 

12 

H. 

19.4 

3 

—      3 

4.7 

3 

+      8 

-  12  =  a    -       1.7        +    0.1 

26 

II. 

7.4 

2 

+      2 

17.2 

2 

4  • 

+     6  =  y+1.7           -    0.1 

27 

T. 

19.6 

3 

0 

8.2 

2 

+      2 

-    3  =  o    —     1.6        +0.9 

March        18 

N. 

22.1 

2 

+      2 

9.2 

2 

+      1 

0  =  a    -  •     1.2        +1.5 

28 

N. 

7.1 

4 

—      2 

19.7 

3 

0 

-2  =  y    +    1.7          -    0.8 

80 

II. 

21.8 

2 

+      2 

11.1 

2 

—      2 

•     l  =  o     -  -    0.8        +1.7 

29 

H. 

2.5 

3 

—  -      2 

13.5 

4 

+      2 

-    6  =  0    +    1,0        +     1.0 

30 

T. 

21.8 

3 

0 

10.7 

3 

0 

•    l  =  a    -  -    0.9        +1.7 

April            2 

H. 

2.9 

3 

—      3 

12.3 

3 

+       1 

-6  =  0    +    0.8        +1.7 

2 

H. 

9.5 

2 

+      2 

18.6 

2 

+      2 

•1  =  7    +     1.6        —    0.9 

3 

T. 

0.4 

2 

—      3 

12.1 

3 

—      2 

-2  =  o     +     0.2        +1.9 

5 

H. 

2.4 

2 

—      2 

11.2 

2 

+      2 

-6  =  0     +     0.4        +1.7 

6 

T. 

1.0 

3 

+      4 

12.9 

8 

1 

+     3  =  0     +     0.6        +1.7 

13 

N. 

22.8 

2 

—      2 

11.1 

3 

0 

-    3  =  a    -  -    0.  6        +1.8 

17 

T. 

4.4 

2 

1 

15.1 

3 

+      5 

-8  =  0    +     1.5        +1.1 

18 

II. 

0.0 

2 

—      2 

11.1 

3 

+       3 

-    6  =  a    -  -    0.3        +1.9 

18 

11. 

4.1 

2 

—      2 

14.0 

2 

0 

4  =  0    +     1.3        +     1.3 

26 

H. 

2.8 

3 

—      5 

13.0 

4 

+      4 

-  11  =0    +     1.0        +     1.6 

May              9 

N. 

4.3 

5 

—      5 

14.1 

5 

+      4 

-12  =  0    +     1.3        +1.2 

17 

H. 

0.4 

2 

+      2 

12.4 

4 

—      3 

+    3  =  a    +    0.2        +1.9 

18 

T. 

1.2 

2 

+      4 

14.1 

2 

+      3 

•    1  =  0    +    0.9        +1.7 

18 

T. 

6.0 

•    3 

—      5 

17.1 

3 

0 

-    8  =  0    +     1.8        +     0.2 

23 

N. 

11.0 

7 

—      3 

21.4 

4 

+      2 

-6  =  7     +     0.9        —1.6 

24 

II. 

1.2 

3 

li 

12.2 

5 

+       4 

-  12  =  o     +     0.  4        +     1  .  - 

31 

11. 

2.3 

4 

o 

14.2 

5 

+       1 

-5  =  o     +     l.l        +1.5* 

June            1 

N. 

1.6 

4 

+       2 

15.0 

2 

—      2 

+     2  =  a     +     1.1         +1.5 

1 

V 

(Cs 

5 

—      2 

1  :>.!) 

3 

+       1 

-6  =  0     +     1.7        +0.3 

4 

T. 

1.9 

2 

~"  ~~             «J 

13.8 

5 

1 

-6  =  0     +     1.0        +1.6 

4 

T. 

7.6 

2 

4 

17.4 

2 

+     12 

-  19  =  0     +     l.s        —    0.3 

5 

a. 

1.9 

3 

0 

13.8 

3 

+       2 

-3  =  a     +     1.0        +1.7 

8 

N. 

1.6 

3 

+      3 

12.3 

3 

—      5 

+     7^a     +     0.5         +1.7 

16 


POSITIONS    OF   FUNDAMENTAL   STARS. 


Date. 

Obs. 

Hour. 

No.of 
stars. 

Mean 
corrcc'n. 

Hour. 

No.of 
stars. 

Mean 
correc'n. 

Ktjnation  of  condition. 

1867. 

Juno           10 

N. 

5.2 

2 

+       1 

16.6 

2 

+       4 

-    5  =  a    +     1.8  a     +     0.66. 

10 

T. 

0.8 

2 

+      3 

12.4 

2 

4 

+     7  =  7    +     0.3        +1.9 

11 

T. 

1.4 

6 

7 

13.7 

5 

0 

-8  =  7     +     0.8        +1.7 

11 

T. 

7.5 

3 

—      5 

17.4           3 

+       8 

-10  =  0     +     1.8        —     0.2 

13 

N. 

3.3 

4 

+      3 

16.6 

3 

+      2 

.     ]=a     +     1.6        +     1.0 

14 

H. 

4.4 

4 

—      7 

16.2 

5 

+       5 

-  14  =  a     +     1.7        +     0.  9 

15 

T. 

0.5 

2 

+      7 

13.6 

2 

—      6 

13  =  y    +     0.  6        +1.8 

20 

N. 

4.4 

2 

—      5 

16.3 

3 

+      1 

-    8  =  a     +     1.7        +     0.8 

20 

N. 

7.5 

2 

—      4 

18.4 

2 

+      8 

-  15  =  /J    +1.9          -    0.5 

21 

H. 

.4.1 

2 

—      6 

15.9 

4 

+      2 

-  10  =  a     +     1.6        +1.0 

21 

H. 

7.5 

2 

—      8 

18.5 

3 

+      9 

-  20  =  p    +     1.9        —    0.  6 

July              1 

N. 

3.8 

3 

+      1 

17.0 

3 

1 

0  =  a     +     1.7        +0.8 

2 

H. 

5.1 

3 

4 

14.0 

2 

+      6 

-  12  =  a     +'    1.  4        +     0.  1 

10 

T. 

5.3 

3 

—      3 

16.9 

5 

1 

-    4  =  a     +     1.8        +     0.5 

.11 

N. 

4.4 

3 

—      9 

16.8 

4 

+      6 

-  17  =  a  .  +     1.7        +     0.  7 

11 

N. 

8.9 

4 

—      8 

19.6 

4 

+     12 

-23  =  /3    -{      1.6           •     1.1 

15 

N. 

5.6 

4 

1 

16.5 

3 

+      8 

-ll  =  a     +     1.8        +0.5 

17 

T. 

5.4 

4 

—      8 

17.  5 

3 

+   10 

—  20  =  a     +     1.8        +     0.  3 

17 

T. 

9.9 

3 

—      8 

20.3 

3 

+      8 

-  19  =  ,3     +     1.3           -1.4 

18 

N. 

9.8 

3 

—      3 

19.9 

3 

+      5 

—  11  =  p    +     1.3        —     1.3 

19 

H. 

5.6 

6 

4 

18.7 

4 

+      5 

-ll  =  a     +     1.8        —    0.1 

19 

H. 

10.1 

2 

—      8 

21.7 

3 

+      2 

-  13  =  p    +     1.  1        —1.6 

20 

T. 

5.4 

4 

—    11 

18.3 

3 

+      2 

-  15  =  a     +     1.  8        +     0.  1 

22 

X. 

5.9 

5 

—      6 

17.9 

5 

+      5 

-13  =  o     +     1.8                0.0 

23 

H. 

5.2 

6 

—      6 

18.8 

3 

+     12 

—  20  =  a     +     1.8                0.0 

24 

T. 

5.8 

3 

—      7 

18.6 

3 

+      7 

—  16  =  a     +     1.  9           -    0.  1 

27 

T. 

5.5 

3 

—      5 

18.7 

2 

+      4 

-ll  =  a     +     1.9                0.  0 

30 

H. 

6.1 

3 

11 

18.7 

2 

+      6 

—  19  =  a     +     1.  9        —    0.  1 

30 

H. 

11.4 

2 

—      2 

21.6 

3 

+   10 

—  15  =  /3    +     0.7                1.7 

31 

T. 

6.9 

2 

—      8 

22.0 

2 

+      4 

—  14  =  n     +     1.4            -1.1 

31 

T. 

12.6 

2 

0 

23.9 

2 

+      2 

—    5  =  /3    -  -    0.2           -1.8 

August        5 

N. 

8.8 

3 

4 

18.3 

3 

+       3 

—    9  =  a     +     1.6        —    0.8 

9 

H. 

7.0 

2 

6 

17.8 

3 

+       7 

—  15  =  a    +     1.8          -    0.2 

12 

N. 

7.6 

2 

—      8 

20.2 

3 

+      6 

-16  =  a     +     1.6           -1.0 

13 

H. 

7.4 

4 

—      3 

20.0 

2 

+       6 

—  11  =  a     +     1.6        —     0.9 

23 

H. 

12.2 

2 

.     12 

22.2 

5 

+      6 

_  21  =  ,3     +     0.  4            -1.7 

23 

H. 

18.7 

2 

4 

(1.2 

2 

7 

+     3  =  y    —     1.9        +     0.  3 

26 

R. 

10.4 

2 

—       1 

22.0 

4 

0 

.     4  +  /3     +     0.9           -1.7 

30 

H. 

7.5 

4 

4 

19.8 

3 

+      8 

—  14  =  a     +     1.7        —     0.9  • 

31 

T. 

8.5 

2 

4 

19.8 

2 

+       5 

—  11  =  0     +     1.6           -1.1 

September  4 

T. 

12.8 

3 

—      8 

22.8 

3 

+       4 

-15  =  0     +     0.1            -1.8 

G 

N. 

10.4 

3 

.     10 

22.9 

6 

+      4 

—  16  =  o     +     0.  7            •     1.  7 

11 

T. 

9.6 

3 

—      9 

20.9 

4 

+       « 

-17  =  a     +     1.2                1.4 

11 

T. 

13.3 

2 

—      6 

0.2 

2 

+      6 

—  15  =  0    —    0.4           •     1.9 

12 

N. 

8.8 

3 

14 

20.2 

6 

+      6 

-22  =  a     +     1.5                1.2 

12 

N. 

14.0 

2 

—     10 

0.3 

2 

+      9 

-22  =  0    --     0.6           -1.7 

13 

H. 

9.4           4 

7 

19.6 

4 

+      6 

—  15  =  a     +     1.4           -    0.1 

13 

H. 

13.  5           4 

4 

23.3 

3 

+       7 

_  14  =  0    -  -    0.2                1.8 

17 

II. 

9.8           4 

—      6 

21.7 

3 

+       8 

_16  =  o     +     1.1        —     1.6 

1 

POSITION'S    OK    FUNDAMENTAL    STARS. 


17 


Date. 

(IllS. 

Hour. 

No.of 

-l;ll~. 

Menu 
colTrc'n. 

lluiir. 

Xo.or 

-t:u~. 

Mi-mi 
oorrec'n. 

Kipiiition  of  condition. 

186T. 

•* 

S'lllclllh'rlf* 

T. 

!i.  •" 

4 

•     12 

•-"-'.  •! 

9 

4      4 

-18  =  a    +     1.0           -1.7 

111 

V 

y.7 

3 

:t 

20.8 

3 

0 

-5  =  a    +     (i.!)           -1.7 

19 

N. 

ii.  i 

2 

+      4 

23.6 

2 

4      2 

0  =  0    -  -    0.5        —    1.7 

22 

11. 

;i.  :; 

6 

1(1 

21.7 

5 

4      8 

-20  =  o    +     1.2               1.5 

24 

T. 

14.11 

2 

—      2 

22.8 

2 

0 

-    5  =  0       -    0.2           •    1.7 

October        1 

11. 

1(1.2 

4 

13 

91.6 

4 

4     12 

-26  =  a    +     l.ll               1.6 

1 

H. 

1  1.- 

4 

—      8 

24.2 

2 

4    12 

-22  =  0    --    0.7        —    1.6 

•-' 

T. 

10.7 

4 

6 

.  19.3 

3 

+       4 

-11  =  0    +     1.2               1.2 

8 

H. 

10.6 

4 

—      7 

22.5 

2 

4-    10 

-  18  =  a    +     0.  8        —     1.8 

8 

H. 

14.6 

2 

2 

1.4 

2 

+      8 

-  12  =  ,  a  -  •   i.o        .1.7 

11 

II. 

10.6 

9 

G 

21.9 

3 

4      4 

-  11  =  0     +     0.9  .             1.6 

14 

11. 

11.4 

2 

12 

21.6 

3 

4      3 

-16=0    +    0.8        —    1.7 

14 

H. 

15.6 

3 

4 

1.8 

5 

4      4 

-  10  =  0    -       1.2               1.4 

1C 

T. 

11.4 

2 

—      2 

1.6 

3 

4      4 

-    7  =  o    -  -    0.2               1.7 

17 

H. 

15.  9 

4 

1 

3.3 

5 

—      2 

1  =  0    -  •    1.5     .  --    1.2 

18 

A. 

15.0 

2 

—       3 

1.9 

3 

—      3 

-    2  =  0    -       1.2           •     l.G 

19 

T. 

11.4 

2 

7 

1.1 

4 

4      3 

-  11  =  a    -  -    0.  1                1.  9 

23 

H. 

ir..  !i 

4 

0 

2.1 

3 

1 

•    1  =  0    -  •    1.3               1.3 

24 

A. 

16.3 

3 

4      1 

3.8 

3 

4-     1 

-    2  =  0    -  •    1.6        —    1.0 

26 

11. 

12.2 

2 

—      9 

22.0 

3 

4-      5 

-15  =  o    +    0.4               1.7 

NoYrllllMT     f> 

A. 

13.0 

2 

+      2 

22.3 

3 

4      l 

0  =  o    +    0.  1           -    0.  7 

:. 

A. 

15.9 

2 

+      8 

2.4 

2 

•    10 

+  16  =  0-1.4           -1.3 

G 

T. 

15.4 

2 

—      5 

2.1 

3 

0 

-    7  =  0    -  •    1.2           -1.4 

15 

A. 

17.8 

9 

+     10 

6.6 

3 

1 

+    9  =  0    -  •     l.f        +0.1 

18 

H. 

13.5 

4 

—      2 

0.6 

3 

+      3- 

-    6  =  a    -  -    0.6                1.7 

18 

11. 

18.  0 

2 

4-     2 

3.6 

2 

0 

0  =  0    -  •    1.8          -0.6 

20 

T. 

13.6 

9 

11 

1.2 

2 

4    12 

—  24  =  o    --    0.7        —    1.8 

26 

A. 

14.5 

4 

-      2 

2.9 

6 

4     2 

—    5  =  a-1.3               1.5 

30 

T. 

15.2 

3 

4 

1.5 

2 

0 

-    5  =  o    -       1.1           -1.5 

Dt'uciuln'r    5 

H. 

15.6 

2 

4      2 

0.8 

2 

0 

+     1  =  a    -       1.0               1.5 

5 

H. 

19.2 

7 

0 

4.2 

2 

4 

+    2  =  0    -       1.7          -    0.2 

7 

T. 

15.2 

3 

+       3 

1.3 

4 

(1 

+    2  =  o    -  •    1.1           -    1.6 

7 

T. 

19.3 

3 

4-     :i 

4.0 

9 

7 

+     8  =  0    -  •     1.7           -     0.1 

11 

H. 

14.0 

4 

+     -I 

1.2 

4 

—      2 

+     5  =  o--    0.9        —     1.7 

!l 

H. 

19.5 

:! 

4     3 

4.4 

9 

—      6 

+     7=0    -  •     1.7                0.0 

16 

H. 

1  :,.-.' 

4 

it 

0.8 

4 

—      6 

+     5  =  o    -  -    0.9        —     1.6 

17 

A. 

17.0 

9 

0 

6.0 

4 

4 

+     3  =  a    —     1.8                0.0 

19 

H. 

16.3 

2 

4     4 

1.8 

4 

4 

+    7  =  a-1.2               1.4 

23 

H. 

15.  3 

5 

4      1 

2.8 

4 

0 

0  =  a    -       1.4               1.4 

•26 

H. 

19.8 

2 

+      2 

6.0 

3 

—      2 

+    2  =  0    -  •    1.8        +0.5 

18 


POSITIONS    OF    FUNDAMENTAL,    STABS. 


In  discussing'  these  equations  the  results  for  the  two  years  arc  first  treated  separately.  Equal 
weight  is  given  to  each  equation,  it  appearing  that  the  error,  arising  from  an  insufficient  number  of 
stars,  is  generally  small.  The  equations  are  treated  by  the  method  of  least  squares,  except  that 
only  the  factors  0,  1,  and  2  have  been  used  as  multipliers.  Thus,  the  following  normal  equations 
and  solutions  are  obtained  : 


Class  a 


1866. 

9* 

70  a  +    32.7  «  —    16.4  b  =  — 1.13 
40  u  +  142.2  a  +    1,'3.8  I  =  —  4.04 
—  20  «  +      7.9  a  +  129.0  b  —  +  ,'3.99 


Solution. 

8. 

a  =  +  0.007 

a  =  —  0.034 
b  =  +  0.034 


48  ft  +      5.1  a—     7.9  b  =  —  0.80 
Glass  p  •{       10  ft  +    91.G  a  +     2.9  b  =   -  2.75 
_    8  ft  +      7.5  a  +    83.4  b  =  +  1.98 


ft  =  —  0.009 
rt  =  —  0.030 
b  =  +  0.020 


21  Y—     2.6  a—    15.16  =  — 0.83 
Class  Y  {  —   2  r  +    24.9  a  +    13.G  b  =  +  0.10 
_  18  r  +    17.2  a  +    54.0  6  =  +  1.48 


r  =  —  0.022 

«  =  — 0.013 
&  =  +  0.031 


The  small  values  of  a,  /9,  and  f  show  that  during  the  year  1866  there  was  no  appreciable  diur- 
nal inequality  in  the  apparent  course  of  the  stars  over  the  meridian,  as  measured  by  the  instrument 
and  clock. 

The  mean  values  of  «  and  6  show  that  the  right  ascensions  of  the  American  Ephemcris,  which 
are  the  same  with  those  of  Dr.  Gould's  standard  Coast  Survey  Catalogue,  require  the  systematic 
correction, 

•_  o».030  sin  «  +  0".030  cos  «. 

The  corrections  applied  to  this  catalogue  to  obtain  the  clock  correction  is  of  the  systematic 
form 

—  0".008  sin  a. 
so  that  the  correction  to  be  applied  to  the  adopted  positions  is 

—  Os.022  sin  a  +  09.030  cos  «. 
1867—  Normal  equations. 


77  «  +    20.0  a—    12.76  =  — 0.35 
Class  a  <;       31  a  +  105.8  a  —     8.3  6  =    -  7.42 
_20a—     0.4  a  +  134.46=  +  4.23 


Solutions. 

8. 

a  =  —  0.009 

a  =  —  0.031 
b  =  +  0.021 


f       49/5—  2.2  a—  18.56=    -3.54 

Class  /?  <J     -2/3+  80.3  a+  11.26==   -3.19 

[  _  22  ft  +  15.5  a  +  90.1  6  =  +  3.88 

C       12  Y  +  5.4  a,  —  2.2  6  --  —  0.29 

Class  r  \        fir+  -°-3 «  +  1.7  6  =  —  0.04 

[  _    3  r  +  3.0a+  27.0  6  =  +  0.02 


•t  =  —  0.062 
a  =  —  0.045 
6  =  +  0.033 


POSITIONS    OF    FUNDAMENTAL    8TAKS.  19 

The  tMiuatioiis  in  ;-  art',  with  one  except  ion.  all  found  in  tin-  first  half  of  tin-  year,  and  will  there- 
fore not  suffice  to  give  reliable  independent  values  of  the  unknown  quantities.  The  values  of «  and 
b  from  the  other  equations  give  (lie  systematic  correction  to  the  adopted  right  ascensions  of  clock 
stars 

—  (I'.O.'M  sin  «  +  Os.O:>.->  cos  « . 

i  omliining  this  with  the  above  correction  Iroin  the  observations  for  ISiiii,  we  have,  for  the -result 
of  both  years'  work. 

—  0".028  sin  «  +  Os.028  cos  «, 
or. 

+  Os.0,'!9  siu  («  —  in1') 

The  very  large  values  of  ./  and  ,;  corresponding  to  the  year  1867  are  remarkable.  They  indi- 
cate that  during  tliis  year  stars  observed  in  the  day-time  seemed  to  cross  the  meridian  too  soon  by 
Os.(l(i.">,  when  compared  with  transits  at  night.  Any  diurnal  inequality  in  the  clock  rate  during  this 
year  has  been  shown  to  be  out  of  the  question,  and  it  does  not  seem  possible  that  the  instrument 
could  have  been  subjected  to  such  unequal  heating,  from  any  cause  whatever,  as  would  change  its 
pointing  in  right  ascension.  The  inequality  is  greater  in  the  case  of  the  forenoon  observations, 
made  before  the  sun's  rays  had  had  time  to  heat  up  the  interior  of  the  roof,  than  in  the  afternoon. 

It  would  therefore  appear  that  the  cause  is  to  be  sought  for  in  the  manner  in  which  observers 
themselves  arc  a  flee  ted  by  the  different  conditions  under  which  the  day  and  night  observations  are 
made.  In  the  day-time  the  nervous  system  is  braced  by  the  rest  of  the  preceding  night,  and  stim- 
ulated by  sunlight ;  the  observations  are  so  few  that  particular  attention  can  be  concentrated  on 
each,  and  this  concentration  is  the  more  easy  from  the  Hue  and  sharp  definition  of  the  transit  wires 
upon  the  bright  ground  of  the  sky.  As  night  advances  the  nervous  system  becomes  relaxed  by  con- 
tinned  labor;  attention  is  no  longer  concentrated  as  during  daylight,  but  is  divided  among  rapidly- 
recurring  observations,  and  the  wires  are  comparatively  indistinct  upon  the  feebly-illuminated  back- 
ground. All  these  causes  will  tend  toward  allowing  the  observer  to  let  the  star  slip  by  a  little  at 
night,  and  this  is  the  very  result  which  is  indicated  by  the  sensible  magnitude  of  the  quantities  a 
and  ,;. 

If  this  explanation  be  the  true  one  we  might  expect  the  work  of  different  observers  to  exhibit 
the  phenomenon  in  question  in  different  degrees.  Taking  the  mean  values  of  the  J's  of  the  class  « 
and  ,J,  which  pertain  to  observers  K,  H.,  and  T.,  during  the  first  nine  months  of  1S67,  we  find  that 

H. 

ForH J=  —  0.106 

For  N J  =  —  0.063 

For  T J  =    - 0.0"..-. 

Itegarding  the  irregular  differences  between  the  products  of  a  and  b  by  their  coefficients  in  the 
equations  of  condition  as  accidental  errors,  which  we  may  well  do,  the  differences  between  the  values 
of  J  indicate  similar  differences  between  the  values  of  the  diurnal  inequality  given  by  the  work  of 
the  several  observers.  That  is  to  say,  the  mean  value  of  «  and  ,5  given  by  the  work  of  H.  is  five- 
hundredths  of  a  second  greater  than  that  given  by  the  work  of  T. 

The  principal  difficulty  in  the  reception  of  this  explanation  arises  from  the  circumstance  that 
no  such  inequality  is  exhibited  in  the  observations  of  1866.  For  the  difference  I  can  give  no  reason 
except  this:  that  a  much  greater  number  of  observations  of  miscellaneous  stars  were  imposed 
upon  the  observers  during  the  nights  of  ISiiT.  Although  this  would  increase  the  effect  referred 
to,  the  actual  increase  is  much  greater  than  could  have  been  anticipated  as  the  result  of  that 
cause.  It  is  also  worthy  of  remark,  that  had  no  correction  been  applied  to  J  for  diurnal  change 
of  collimation,  there  would  have  been  no  great  discrepancy  between  the  values  of-/  and  ,;  resulting 
from  the  two  years'  work. 

Supposing  the  quantities  «  and  ,';  to  remain  constant  throughout  each  year,  neither  their  mag 
iiitudes  nor  the  causes  whence  they  originate  will  affect  the  quantities  a  and  l>,  on  which  depend 


20 


POSITIONS    OF   FUNDAMENTAL   STARS. 


the  systematic  corrections  to  the  .adopted  star  positions.  But,  if  we  suppose  them  irregularly  varia- 
ble between  wide  limits,  or  subject  to  a  regular  annual  variation,  we  may  satisfy  all  the  preceding 
equations  of  condition  by  zero  values  of  a  and  6,  each  equation  giving  a  separate  value  of  a, ,?,  or  f. 
Whether  there  is  any  reason  to  suppose  them  so  variable  is  a  question  for  the  judgment  of  the  indi- 
vidual astronomer.  The  present  discussion  will  be  continued  on  the  supposition  that  they  are  not 
so  variable,  and  that  the  corrections  indicated  by  a  and  b  are  real. 

Deeming  it  desirable  to  see  what  systematic  corrections  would  be  given  by  the  observations  of 
1868,  their  results  have  also  been  investigated  on  the  supposition  that  the  correction  would  be  of 
the  form 


with  the  result, 


«  sin  («  —  151'), 
ft  =  Os.024. 


If  we  give  half  weight  to  this  result,  owing  to  the  small  number  of  determinations  on  which  it 
depends,  the  definitive  systematic  correction  to  the  adopted  right  ascensions  will  be 

Os.036sin(«  —  lo1'), 
indicating  an  error  of  Os.07  in  the  difference  of  right  ascensions  between  stars  in  I)1'  and  in  211'. 

CORRECTIONS  TO  THE  POSITION  OF  THE  EQUINOX,  AND  TO  THE  OBLIQUITY  OF  THE  ECLIPTIC. 

The  mean  corrections  to  the  positions  of  the  sun  derived  from  Hanson's  Tables,  and  given  in 
the  American  Ephemeris,  are  as  follows.  J  «,  Jp,  and  Jj/  represent  the  corrections  to  the  right 
ascension,  north  polar  distance,  and  ecliptic  polar  distance,  respectively : 


1866. 

1867. 

Aa 

Ay 

A/ 

Aa 

Aj> 

Ap> 

8. 
—  0.08 

+  1.3 

14 

+  1.1 

8. 

+  0.05 

„ 

+  0.1 

II 

+  0.2 

February  
March  

-  0.  04 
—  0.  05 

+  0.7 
—  0.2 

+  0.5 
-  0.5 

+  0.06 
0.00 

+  0.6 
+  1.2 

+  0.9 
+  1.2 

—  0.01 

+  0.8 

+  0.7 

—  0.02 

+  0.8 

+  0.7 

May. 

0.00 

+  0.2 

+  0.2 

-  0.01 

+  1.5 

+  1.5 

June  

+  0.01 

+  0.6 

+  0.0 

+  0.03 

+  0.4 

+  0.4 

July  .- 

—  0.01 

+  0.4 

+  0.4 

+  0.03 

+  0.7 

«MH> 

+  0.02 

+  0.7 

+  0.6 

+  0.02 

+  0.8 

+  0.7 

September  
October  

—  0.01 
-f  0.03 

+  1.4 

+  1.3 

+  1.5 
+  1.1 

+  0.05 
+  0.03 

+  1.5 
+  0.9 

+  1.2 

+  0.7 

November  
December  

-f  0.07 
+  0.04 

+  1.1 
+  0.2 

+  0.9 
+  0.2 

+  0.06 
+  0.09 

+  1.0 
+  1.6 

+  0.8 
+  1.5 

Put 

z  for  the  constant  error  in  the  measures  of  polar  distance ; 
J  u>  for  the  correction  to  Hanson's  obliquity  of  the  ecliptic ; 
'  A  e  for  the  error  of  polar  distance  of  the  ecliptic  at  the  vernal  equinox. 

Then  each  value  of  J  j>'  will  give  an  equation  of  the  form 

=  c  —  J  m  sin  7  —  J  e  cos  /. 


POSITIONS   OF   FUNDAMENTAL   STARS. 


21 


The  equations  tor  cadi  \ear.  \\hen  solved  l»y  least  squares,  will  become,  with  sufficient  approxima- 
tion, 

\->z  l'J,,<: 


(5  Je  r=  —  -  J  p1  cos  /: 

and  the  constant  correction  to  the  right  ascensions  of  stars  will  be 

J  «  =  cosec  M  J  e  =  2.5  J  c. 

The  solution  for  each  year  gives 


1866. 

iaer. 

^      +  0".G2 

+  0".S8 

J  u>  +  0".08 

+  0".03 

J  c  +  0".-li' 

—  0".02 

j«  +  0s  .07 

0s  .00 

The  great  divergence  iu  the  value  of  J  «  for  the  two  years  renders  the  result  somewhat  uncer- 
tain. Considering,  however,  that  the  divergence  may  arise  from  some  cause  acting  iu  opposite 
directions  in  the  two  positions  of  the  instrument,  and  that  the  preceding  four  years' observations 
with  the  old  instruments  (lS(52-'(i"))  indicate  a  correction  of  +  Os.05,  the  correction  +  Os.03  for  the 
position  of  the  equinox  will  be  admitted. 

The  entire  systematic  correction  to  the  fundamental  catalogue  is,  therefore, 

+  Os.0.'i  +  Os.0:5(i  sin  («  —  15h) 

COMl'AIJISON  OF  RIGHT  ASCENSIONS  OBSERVED  DIRECTLY  AND  BY  REFLECTION. 

Each  annual  volume  contains  a  comparison  of  the  direct  and  reflex  observations  of  north  polar 
distance,  but  none  of  the  right  ascensions.  As  a  comparison  of  the  latter  will  decide  with  consid- 
erable probability  whether  the  meridian  to  which  the  observations  are  reduced  is  really  a  vertical 
great  circle,  the  results  of  one  are  here  presented.  The  individual  discordances  in  the  case  of  the 
several  stars  may  be  seen  at  a  glance  by  reference  to  the  means  given  under  the  head  "  Corrections 
to  the  positions  of  stars  in  the  American  Ephemeris."  These  means  were  collected  in  groups,  each 
included  in  a  zone  extending  through  10°  of  polar  distance.  Each  discordance  was  multiplied  by 
sin  X.  1'.  J).,  and  the  mean  by  weights  taken,  with  the  following  results : 


1866. 

1867. 

Limits  of  N.  P.  D. 

\li.-m  f~D        1?^  win  ti 

jHr.ul  ^U  ^—  Kf  Hill  2' 

(D  —  E)8inj> 

wt. 

(D  —  R)slnj> 

Wt. 

o           o 

a. 

i. 

i. 

—   3—2 

+  0.004 

19 

-  0.  Oil 

19 

-  0.004 

+    2—10 

—  0.009 

9 

—  0.002 

20 

—  0.004 

11  —   20 

+  0.003 

28 

+  0.004 

29 

+  0.004 

21  —    30 

+  0.017 

•.'- 

+  0.032 

15 

+  0.022 

31  —    .|.-> 

—  0.028 

19 

0.000 

18 

-  0.014 

.Vi  —     ClI 

-  0.  013 

28 

-  0.034 

25 

—  0.023 

70—    79 

—  0.009 

40 

-  0.010 

39 

—  O.IMI1.! 

80—   89 

—  0.007 

28 

—  0.019 

37 

—  0.  014 

fl>—    99 

—  o.u:;- 

31 

—  0.028 

24 

—  0.034 

99—  in:. 

-  0.  04.1 

0 

+  0.  010 

12 

—  0.008 

22  POSITIONS   OF   FUNDAMENTAL   STARS. 

The  general  result  may  be  summed  up  as  follows :  In  the  north  there  is  a  substantial  agreement 
between  the  transits  observed  directly  and  those  observed  by  reflection.  In  the  south  the  latter 
exceed  the  former  by  the  quantity  08.018. 

If  the  systematic  discordance  depended  entirely  on  the  instrument,  the  algebraic  sum  of  the 
south  discordance  in  one  position  of  the  instrument,  and  of  the  corresponding  north  discordance  in 
the  reverse  position,  ought  to  vanish.  They  do  not  so  vanish.  If,  in  recording  a  transit  by  reflec- 
tion, the  observer  should,  from  his  less  easy  posture,  or  from  any  other  cause,  let  a  swift-moving 
star  slip  by  a  little,  the  result  would  be  of  the  same  character  with  that  actually  found. 

The  above  comparison  seems  to  me  to  indicate,  with  great  probability,  that  the  axis  of  motion 
of  the  instrument  is  subject  to  no  wabbling  amounting  to  as  much  as  Os.02. 

CORRECTIONS  TO  THE  RIGHT  ASCENSIONS  OF  STANDARD  STARS  DERIVED  FROM  OBSERVATIONS  WITH 
THE  TRANSIT  INSTRUMENT  AND  WITH  THE  TRANSIT  CIRCLE. 

The  results  given  in  the  following  table  are  all  in  the  form  of  corrections  to  the  American 
Ephemeris  for  the  years  1865-'C9 ;  the  positions  for  previous  years  being  found  by  carrying  back 
those  found  in  the  American  Ephemeris  for  1809,  with  the  proper  motions  there  employed. 

The  second  column  gives  the  mean  correction  deduced  from  the  observations  with  the  transit 
instrument  during  the  four  years  1862-'G5,  without  correction.  These  are  in  fact,  the  standard 
corrections  employed  in  deducing  the  clock  corrections  for  the  transit  circle.  The  small  figures  in 
this  and  the  third  column  following  indicate  the  number  of  observations  on  which  the  result 
depends. 

Next  we  have  the  amount  of  the  systematic  correction  +  <)*.<).'?  +  0N.03G  sin  (a  —  15'1)  deduced 
from  the  observations  with  the  transit  circle.  The  sum  of  these  two  columns  gives  the  final  cor- 
rection resulting  from  the  observations  with  the  transit  instrument,  found  in  the  next  column. 

Column  "Eesult  of  circle"  gives  the  mean -corrections  resulting  from  the  observations  with  the 
Transit  Circle  during  the  years  186G-'67.  This  column  is  deduced  from  the  corrections  to  the  right 
ascensions  found  in  the  published  volumes  for  those  years,  the  constant  correction,  +  Os.03,  being 
applied  to  the  result. 

Column  C  —  T  gives  the  excess  of  the  transit  circle  result  over  that  of  the  transit  instru- 
ment, to  which  we  shall  recur  presently. 

The  next  column  gives  the  correction  concluded  from  the  work  of  both  instruments.  It  is  formed 
by  giving  to  each  result  a  weight  proportional  to  the  number  of  observations. 


POSITIONS    OF    FUNDAMENTAL   STARS. 

KXimtiT  OF  roi;i;i:(TioNs  TO  THE  KICHT  ASCENSIONS  or  M  \M.\I;I>  STAKS. 


23 


8Ur. 

Transit 
l-i-.-.'-V,:,. 

Sy-li-matii- 

ColTl-ctillll. 

I.V.-nlt  of 
transit. 

KV^nlt  of 

rilrlr. 

C  —  T. 

CnnrliiiliMl 
correction. 

H, 

H. 

.s. 

a. 

t. 

«. 

n      Andromeda' 

4-  .  002,4 

f         .OH 

f       .057 

4-     .037™    • 

-   .020 

f             .050 

;       IVnasi      .       .       . 

-    .017,. 

-f           .  054 

\-       .037 

h    .031,., 

-  .003 

4-           .  035 

ii      Cas.-io|ir:r     . 

-    .08, 

-f-           .051 

-       .03 

.00,0 

f  .03 

.01 

,<     (Vti    .... 

-1-   .o:;i... 

+            .051 

f      .089 

f    .08241 

.000 

f         .o,-*> 

21    ('assio]>i'a-     . 

-    - 

4-    .09,:, 

4-          .09 

I'isrilllll  . 

-    .05-' 

-)-           .049 

—       .  003 

-    .002,., 

4-  .001 

.1111:1 

6    Ceti  .... 

4-     .00161 

+           .nlii 

f       .  047 

4-  .061,, 

f  .014 

4-           .050 

A     Cassioi>f;r     .       . 

. 

. 

. 

. 

V    Piscimu  .     .     . 

-f     JM- 

+          .044 

4-       .092 

4-    ."H6« 

f  .024 

4-           .  103 

a     Piscitim  .      .      . 

-    .039M 

4-        .04:! 

4-    .  .004 

4-    .002*, 

-  .002 

4-         .003 

f}    Arietis    . 

4-    .OO&j, 

4-           .041 

4-       .  047 

4-    .04318 

-  .004 

4-           .  045 

."ill    ('a>Mi>|>r;i>     . 

. 

4-    .04,,, 

.04 

a    Arietis    . 

+    .« 

+           .O:H» 

4-       .  044 

4-    .032K 

-  ."012 

4-           .038 

P    (Vti   .... 

+    .o::i 

+          .oils 

4-       .069 

4-    .070,, 

4-  .007 

4-           .072 

t      Cassio],i-;<.    .      . 

•     - 

-    -. 

4-    -268 

•     • 

+           .26 

y    Ceti   .... 

—    .11117 

+          .034 

4-       .  027 

4-    .03*.,, 

4-  .oil 

4-           .032 

a     Ceti   .... 

4-    .01-:, 

+         .o:!l 

+       .049 

4-    .052^ 

4-  .003 

4-           .050 

48  (H)CViilii    .      . 

. 

. 

4-    .12u 

. 

4-           .12 

f    Arietis    .     .     . 

-    .027,,, 

+           .029 

4-     ."002 

-    .01414 

—  .016 

.007 

a    Pereei     .     .     . 

-    .052,o 

+           .d->f 

—       .  024 

4-   -09,, 

4-  .11 

4-           .04 

il    Tanri 

4-    .0054, 

+            .1^5 

4-       .030 

4-   .04*., 

4-  .018 

4-          .036 

f    Pereei     . 

.  (HK>3 

+         .oi:t 

4-       .023 

4-    .022r, 

—  .(Mil 

4-           .022 

y    Eridani  .     .     . 

+   .o:u.. 

+           .022 

4-       .  053 

4-    .095,, 

4-  .042 

4-           .06* 

y    Tauri      .     .     . 

+   •  "- 

+          .  019 

4-       .  042 

4-     .034.:,, 

—  .008 

4-        .  o:w 

e    Tauri      .     . 

4-    -004*, 

4-          .018 

4-       .  022 

4-    .014,, 

—  .()()« 

4-         .019 

a    Tauri 

4-    .(Mil., 

+          .017 

4-       .018 

4-    .(MHiM 

—  .012 

4-           .014 

i:      (':lllli>liip;ir<li 

. 

4-    .1",:, 

. 

4-          .17 

Auriga-    .      .      . 

—    .031  ;„ 

4-           .014 

—      .  022 

4-    .002,., 

4-  .024 

.010 

11  Orionis    .      .      . 

-    .UK),, 

4-           .013 

—       .  027 

_    .066 

—  .028 

.  037 

a    Auriga-   .     .     . 

-  .or1.,, 

4-           .011 

—       .  0*2 

—    .OSr, 

0 

.03 

;    Orionis   . 

4-    .012,e 

4-        .oil 

4-       .023 

4-    .030« 

4-  .007 

4-          .025 

/3    Tauri      .     .     . 

—    .010TO 

+           .010 

.000 

4-    .029,, 

4-  .029 

4-          .011 

t    Oriouis   .     .     . 

-    .019,, 

4-        .009 

—        .010 

4-   .oifei 

4-  .022 

.004 

a    Leporis  .     .     . 

-    .019,5 

+         .  009 

—       .010 

. 

—           .  010 

s    Orionis  . 

+    .010.,, 

4-           .008 

4-      .018 

4-    .O32.w 

4-  .014 

4-          .023 

a    Columbia     . 

-    .061,6 

+           .007 

—      .  054 

—    .030a 

4-  .024 

.050 

a    Orionis   .     .     . 

-    .003,,, 

4-          .007 

4-       .004 

.000.* 

—  .004 

4-           .003 

H    Geuiiuur      .     . 

—  .002,. 

4-         .004 

+       .002 

—    .029,, 

—  .031 

.008 

y    Geminor 

.  000;,, 

4-          .002 

4-      .002 

—    .005,, 

—  .007 

.(Mil 

51  (H)  d-phci  .     . 

. 

4-    -82« 

. 

+ 

a     Canis  Ma.joris   . 

—    .061« 

4-             .(Nil 

—       .060 

—   .(i::.-,,,. 

-  .025 

—           .051 

e     Canis  Majoris   . 

—    .OiKIa, 

.000 

—     -.023 

-  .oia« 

4-  .005 

.020 

S    Canis  Majoris  . 

—    .018« 

.001 

—       .019 

—    .012s 

-r-  .007 

.016 

•  •    Geminor 

-    J'-'S 

—          .002 

—       .030 

-    .022,, 

4-  .008 

.096 

a2  Gemiuor      ... 

+    .869» 

—            .0(C! 

4-       .266 

4-    .280* 

4-  .014 

+           .  270 

a    Canis   Minoris* 

-    .013,1B 

—       .00:1 

—      .016 

—    .045.M 

4-  .007 

. 

/}    Geminor      .     . 

+    .002*, 

.003 

—        .  001 

—      .00953 

—  .008 

.004 

ij>    Geminor 

—    .040, 

.004 

.044 

-    .056,0 

—  .012 

.050 

3    Ursa*  Miuoris   . 

. 

p    Argus 

—    .085, 

.005 

—       .030 

-    .032,, 

—  .002 

—           .  032 

e     Hydra?    .     .      . 

—    .(KM* 

.006 

—      .010 

-    .012., 

—  .002 

—          .011 

t     Urea?  Majoris    . 

-     - 

•      • 

-     - 

-     • 

o3   Ursa;  Majoris    . 

• 

—      .01,:, 

. 

.01 

K    Caiu-ri    . 

4-  .'oo-j,. 

.'ON 

—      .004 

+    .048,, 

4-  .052 

4-          .019 

1     (H)  Dracouis    . 

.    •  . 

. 

—    .17,, 

. 

—          .17 

a    Hydne    . 

-   .001 

.006 

—      .007 

4-    .005,, 

4-  .012 

.000 

d    Ursa:  Majoris    - 

-     - 

6    Ursa!  Majoris    . 

4-  .If.' 

.006 

4-     .01 

4-    .07., 

4-  .06 

4-          .04 

e    Leonis    . 

—   .01:!  . 

—          .006 

—      .019 

-     .0303T, 

—  .011 

-           .  025 

/i    Leonig    .     . 

+    .045», 

—          .  005 

4-     .OKI 

4-    .073,., 

4-  .033 

4-           .051 

a    Li-onis 

-   .004* 

.III  15 

—      .009 

-    .0226, 

—  .013 

.015 

32  l"r.-a-  Majoris    . 

• 

• 

• 

• 

• 

•  In  the  case  of  a  Caiiis  Miuoris  the  correction  i  ;.«03G  ban  been  applied  to  C  —  T  on  account  of  the  inequality  of  proper  motion  given  by  Anwcrs. 


2-1.  POSITIONS   OF   FUNDAMENTAL   STARS. 

EXHIBIT  OF  CORRECTIONS  TO  THE  RIGHT  ASCENSIONS  OF  STANDARD  STARS— Continued. 


Star. 

Transit 
1862-'65. 

Systematic 
correction. 

liV.sillt  Of 

transit. 

Result  of 
circle. 

C  —  T. 

Concluded 
correction. 

8. 

s. 

w. 

*. 

e. 

H, 

y    Leouis    .     .     . 

4    .0176, 

.004 

-f       .  013 

4    -017:H 

4  .004 

4          .014 

9    (11)  Draconis   . 

. 

. 

—    .08, 

. 

.08 

p    Leonis    . 

-    .036,8 

.003 

-       .039 

-    .034,4 

4  .005 

.037 

t     Leonis    . 

4    .07335 

.003 

-)-       .070 

4    .081*, 

4  .oil 

4           .074 

a     Urea;  Majoris    . 

h    .001*4 

.002 

-       .001 

4    -OS,, 

4  .03 

4          .01 

i!    Leonis    . 

—    .02055 

.001 

-       .  021 

-    .08844 

—  .017 

—          .028 

(i    Crateris  . 

4    .005,0 

0 

+       .  005 

4      .004,,; 

-  .001 

4           .  005 

T    Leonis    . 

h    .00713 

+           .001 

H-     .  oiw 

4    -015,5 

4  .007 

4           .012 

A    Draconis      .     . 

. 

. 

. 

4      .19l9 

. 

.19 

v    Leonis    .     .     . 

-    .01237 

+           .002 

—       .010 

—    .005,9 

4-  .005 

.008 

3    Leonis    . 

H-    -Oil,* 

4          .002 

+       .013 

4    -019.50 

4  .006 

4          .015 

y    Ursse  Majoris    . 

h    .039,! 

+           .003 

+      .04 

4    .07,,-, 

h  .03 

4           .07 

o     Virginia  . 

-    .0613i 

+          .005 

—      .056 

—    .034,0 

h  .022 

.047 

4    (H)  Draconis    . 

. 

—    .06,, 

. 

;/     Virginis  .     .     . 

-      .01138 

4          .006 

—      ."005 

4    .0193, 

4  .024 

4           .'006 

/?    Corvi      ...     . 

+    .064*-, 

4          .008 

+      .072 

4   .100* 

4  .028 

4          .087 

K  .Draconis 

4    -026 

. 

4          .02 

32-  Camelopardi     . 

. 

4    -50» 

. 

.50 

a    CanumVenat.  . 

4       .011.2, 

+          .010 

+      .021 

4      -03049 

4  .009 

4           .(127 

0    Virginis  - 

-    .031s, 

+          .012 

—      .019 

4    -006,0 

4  .025 

.013 

a    Virginis  - 

+    .006,00 

4          .014 

+      .020 

4    -007V, 

—  .013 

4          .015 

f    Virgiuis  . 

4    .0046, 

+          .016 

+      .020 

4      -04143 

4  .021 

4           .029 

t/    Ursse  Majoris   . 

—    .094 

4          .02 

—       .07 

4    -02,0 

4  .09 

.00 

71    Bootis     - 

—    .030M 

+          .019 

—       .011 

—    .023*,- 

—  .012 

.017 

a    Dracouis      .     . 

-     - 

4    -03;3 

-     - 

4          .03 

a    Bootis     . 

+    .013,.,, 

+          .  023 

+      .036 

4    .033,B 

—  .003 

4           .  035 

0    Bootis     - 

+    .  0435 

+          .024 

-)-       .067 

4    .H9ia 

4  .052 

4           .082 

5     Ursse  Miuoris    . 

. 

. 

4    -13,3 

. 

4        .13 

e     Bootis     .     .     . 

—    .018«, 

4          .026 

+       ."008 

4    -Oils, 

4  .003 

4          .009 

a-   Libra; 

—    .021;,.. 

-r-           .027 

+       .006 

4    .040M 

4  .034 

4         .016 

j3    Ursse  Miuoris    . 

-    .OU4 

+          .03. 

+      .02 

4    -03,:, 

4  .01 

4          .02 

ft    Bootis     .     .     . 

_ 

. 

. 

-    .06,, 

.06 

;3    Libra? 

—      .010,,; 

4           .031 

+      .  021 

4    .052% 

4  .031 

4          .031 

ft    Bootis     .     .     . 

-    .004,, 

4          .032 

+      .028 

4    .012,, 

—  .016 

4           .018 

}•-  Ursje  Miuoris   . 

—    .07,, 

-     - 

.07 

a    Coronie  Boreal  is 

.  000,,, 

+          .034 

+       .034 

4    .021« 

—  .013 

4          .028 

«    Serpeutis 

.  ooow 

4           .035 

+      .035 

4    .06947 

4  .034 

4          .051 

c     Serpentis     .      . 

—    .011,,, 

4          .036 

+      .  025 

4    -025i9 

.000 

4          .025 

f    Ursa?  Minoris    . 

4    -15,3 

.15 

&    Scorpii   .     .     . 

+    .004"ra 

+          "038 

+      ."042 

4    .040,, 

—  ."002 

4          .041 

/31  Scorpii    . 

4    .054,, 

.039 

4-      .093 

4    -106,., 

4  .013 

.101 

6    Ophiuchi     .     . 

+    .017,0 

+          .040 

4      .057 

4    .049,7 

—  .008 

4          .052 

T    Herculis.     .     . 

4    -21.8 

. 

.21 

a    Scorpii    .     .     . 

—    ."021« 

4           .  042 

4      .021 

4    .020,, 

—  .001 

4          .021 

11    Draconis      .     . 

—    .47, 

+           .04 

.43 

-'.774 

-  .34 

.60 

A    Dracouis 

. 

—    .017 

.01 

f    Ophinchi      .     - 

—    .050,4 

+           .  043 

—       .007 

4    .018,, 

4  .025 

4         .005 

ij    Herculis. 

. 

. 

4    -04,8 

.04 

K    Ophiuchi     .     - 

+    .0283,1 

4           .047 

4       ."070 

4    .067,, 

—  ."003 

4          .069 

(I    Herculis 

10     Ursse  Miuoris    . 

—    .08,, 

.08 

a    Herculis. 

+  ."OOIM 

4          .  049 

4       .050 

4    -0464, 

—  .004 

4          .049 

6    Ophiuchi 

—    .002« 

4.           .050 

4       .048 

4    .071,, 

4  .023 

4           .  057 

a    Ophiuchi 

+    -01285 

.051 

4      .063 

4      .06153 

—  .002 

.062 

u    Draconis      .     . 

. 

.     . 

.     . 

4    .06,0 

-     - 

4          .06 

fi    Herculis. 

—    .007W 

+          .052 

4       .045 

4    .023., 

—  .022 

4          .034 

4l  Draconis      .     . 

_ 

. 

—    .055 

—          .05 

y    Draconis      .     . 

+    .05, 

4          .05 

4     .10 

—    .  05,, 

—  ."l5" 

—            .III! 

y*   Sagittarii     .     . 
/t1   Sagittarii    . 

—    .02918 
—    .023s, 

.054 
4          .055 

4       .025 
4      .032 

4    -0777 
4    .057,, 

4  .052 
4  .025 

4           .040 
4           .  035 

6    Ursse  Minoris    . 

, 

. 

. 

r/    Serpeutis     .     - 

+    ."011,3 

4          .056 

4      .'067 

4   .H*. 

4  .045 

4          .085 

1    Aquilse    .     .     . 

+    .03374 

4          .058 

4      .091 

4    -122.7 

4  .031 

4          .097 

a    Lyrse.      .      .     . 

+      .OOlse 

+          .058 

4      .059 

4    .044,, 

—  .015 

4          -051 

/}    Lyra.     .     .     . 

+    .01545 

+          .060 

4      .075 

4    .031,0 

—  .044 

4         .061 

POSITIONS    OF    FUNDAMENTAL    STARS. 

INHIBIT  OK  roi;i;i:rnoNs  TO  Tin:  I;K;IIT  ASCKNSIONS  OF  STANDARD  STARS— Contiim.-.i. 


Star. 

Traii-it 

Systematic 
correction. 

Result  of 
transit. 

Result  of 
circle. 

C  —  T. 

Concluded 
correction. 

». 

ft 

ft 

ft 

t. 

i. 

r.     Sajjittarii     . 

—    .024s, 

4-           .060 

4-      .036 

4-    •  0351:! 

-  .001 

4-        .  O3t; 

.">o  Draeoni.f 

_ 

. 

i            tyt 

, 

4~         .  •*•* 

i       04't 

4-          .061 

4-      .  104 

111 

4-  .007 

.  11  Hi 

</     Sagittarii     .      . 

—    .IIT-J 

4-        .  oty 

—      .010 

. 

.010 

it     Dracouis      .     . 

-    - 

4-  .  lo,5 

4-        .10 

T    Draconis 

. 

4-    -21, 

4-        .21 

<i     Aquila)    . 

4-  .  oi2<« 

4-          .'062 

4-       "074 

4-    .096.37 

4-  .022 

.  OKi 

K      AqililiO    .       .      . 

-    .005,7 

.063 

4-      .058 

4-  .100,9 

4-  .042 

.075 

y    Aquilie   .     -      - 

4-  .005.. 

4-           .063 

4-      .068 

4-    .043,0 

—  .025 

.059 

a    Aquihe   .     .     . 

4-    .Oil* 

4-          .064 

4-      .075 

4-    .069« 

—  .006 

4-          .073 

e     Draeonis 

4-    .  186 

4-          .18 

Aqnihr    . 

.oo6« 

4-           .064 

4-      ."064 

4-    !  054,9 

-  .'OIO 

4-          .062 

).     Ursa1  Minoris    . 

. 

. 

+    -12s, 

4-        -12 

r     Aquilic   . 

—    .098, 

4-           ."065 

—       .033 

—    .033,., 

."OOO 

.033 

a*  Caprii     .     .     . 

-    .00760 

4-           .065 

4-      .058 

4-   .099,,, 

4-  .041 

4-           .070 

K    Cephei    .      .     . 

. 

. 

4-    .24,. 

4-           .24 

xr    Caprii     .     .     . 

. 

. 

. 

4-    -05690 

. 

+           .056 

e     Dclphiu!      .     . 

4-   .010,, 

4-          .066 

4-      .076 

4-    .082,9 

4-  .006 

4-           .079 

a    Cygni     .     .     . 

4-  .002,3 

4-           .  066 

4-      .068 

4-    .040*, 

—  .028 

4-           .  057 

fi    Aquarii  .     .     . 

4-    -021,, 

4-          .066 

4-      .087 

4-    -123,7 

4-  .036 

4-          .098 

v    Cygni     .     .     . 

4-    .033S 

4-          .066 

4-      .099 

4-    .083,9 

—  .016 

4-           .086 

61  Cygni     .     .     . 

. 

4-    .  350K 

_ 

4-           .  350 

(    Cygui     .     .     . 

-    .01261 

4-          .066 

4-      .054 

4-      .01533 

—  .039 

4-           .038 

a    Cephei    .     .      . 

4-  -051B 

4-          .07 

4-      .12 

.00^ 

—  .12 

.04 

1    Pegasi    .     .     . 

—    .074, 

4-          .066 

—      .008 

-    .052,7 

—  .044 

—          .037 

/3    Aqnarii  . 

—    .OOSso 

4-          .066 

+      .061 

4-    .0643, 

4-  .003 

4-          .062 

i1    tvplii-i    .     .     . 

4-    -025, 

4-          -07 

4-      .09 

4-    -12,8 

4-  .03 

4-        .10 

f     Aquarii  .      .     . 

-    .017,, 

4-          .066 

4-.     .  049 

+    .041, 

—  .008 

4-          .046 

e     Pegasi     . 

—    .014« 

4-          .066 

4-      .052 

4-      -01536 

—  .037 

4-          .037 

11  Cephei    .     .     . 

•     - 

.00,0 

-     - 

.00 

ft    Capricorn!  .     . 

-    .055,7 

4-          .065 

4-      .010 

4-    -032.W 

4-  .022 

4-           .019 

79  Draconis      .     . 

. 

. 

. 

4-    .05, 

4-          .05 

a    Aquarii  . 

—    .011.15 

4-          .065 

4-      .054 

4-    -065:,, 

4-  .Oli 

4-          .059 

ft    Aqnarii  . 

—  .oi:^ 

4-          .065 

4-      .052 

4-    .0542, 

4-  .002 

4-          .053 

-.    Aquarii  . 

—    .0092J 

4-          .064 

+       .055 

4-    -041,9 

—  .014 

4-          .048 

9    Aquarii  . 

4-  .ooi.M 

4-          .063 

4-      .064 

4-    .057.,., 

-  .007 

4-          .061 

226  Cephei    .     .     . 

. 

. 

. 

. 

. 

„ 

f     Pegaai     .     .     . 

4-    .041i3 

4-          .063 

4-      .104 

4-    .082*. 

—  .022 

4-          .093 

t     Cephei    .     .     . 

. 

. 

4-    .12n 

. 

4-          .12 

i    Aquarii  .      .      . 

4-    .060*, 

4-          .062 

4-      .122 

4-    -157,3 

4-  .035 

4-          .134 

a    Piscis  Austral!  s 

-    .012* 

4-          .062 

4-      .050 

4-    .08816 

4-  .038 

4-          .065 

a    Pegasi    . 

4-    .016,s 

4-          .061 

4-      .077 

4-    -040,6 

—  .037 

4-          .060 

o     Cephei    ... 

. 

. 

—    .03, 

. 

—          .03 

"    Piscium  . 

. 

. 

4-    .087,8 

. 

4-          .087 

i     Piscinm  .     .     . 

—    .017« 

4-         .058 

4-      .041 

—    .006,7 

—  .047 

4-          .028 

>'    Cephei    . 

4-    .25,o 

4-         .06 

4-      .31 

4-    -IS, 

4-  .16 

4-          -24 

u    Piscinm  . 

—    .016*, 

4-          .056 

4-      .040 

4-    .031,, 

—  .009 

4-        .  o:t7 

26 


POSITIONS    OF    FUNDAMENTAL    STARS. 


The  column  G  —  T  is  that  which  principally  commands  our  attention.  The  first  feature  to 
be  noticed  is  the  magnitude  of  the  discrepancies.  Taking  their  mean  value,  without  regard  to  sign, 
for  the  109  clock  stars  observed  by  both  instruments,  we  find  it  to  amount  to  0".017.  This  is  a 
greater  mean  difference  than  we  should  expect  to  arise  from  the  purely  accidental  errors  of  obser- 
vation. Let  us  see  how.  far  it  is  of  a  systematic  character,  depending  either  upon  the  right  ascen- 
sion, the  polar  distance,  or  the  magnitude  of  the  star. 

Dividing  the  circle  of  E.  A.  into  eight  parts,  we  find  the  following  mean  value  of  C  —  T  for  the 
clock  stars  of  each  octant : 


Octant. 

C  —  T 

1 

8. 

+  0.002 

2 

+  0.007 

3 

-  0.006 

4 

+  0.008 

5 

+  0.012 

6 

+  0.007 

7 

+  0.010 

8 

—  0.010 

We  see  that  the  circle  results  are,  on  the  average,  greater  by  Os.004.  After  correction  for  this 
difference,  the  results  will  indicate  a  cyclical  difference,  of  which  the  largest  term  is  —  Os.005  cos  «, 
but  they  are  not  regular  enough  to  predicate  anything  certain  upon.  It  will  be  remembered  that 
no  corrections  for  cyclical  error  have  been  applied  to  the  circle  results,  and  the  •  somewhat  unex- 
pected result  of  this  comparison  is  that  they  do  not  seem  to  need  any  such  correction. 

Arranging  the  values  of  C  —  T  according  to  polar  distance,  and  taking  the  mean  for  each  ten 
degrees,  we  have  the  following  mean  values  of  this  quantity.  For  stars  less  than  50°  from  the  pole, 
the  mean  by  weights  proportional  to  the  number  of  observations  has  been  taken.  For  the  other 
stars  the  mean  is  taken  indiscriminately. 


Limits  of  N.  P.  D. 

C  —  T 

o 

o 

8. 

10  — 

20 

+  0.05 

20  — 

30 

—  0.03 

30  — 

40 

+  0.01 

40  — 

50 

+  0.02 

50  — 

CO 

—  0.  005 

GO  — 

70 

—  0.006 

70  — 

80 

—  0.  006 

80  — 

90 

—  0.  001 

90  — 

100 

+  0.016 

100  — 

110 

+  0.017 

110  — 

120 

+  0.015 

North  of  the  zenith  (polar  distance  51°)  the  differences  fall  within  the  unavoidable  errors  of  the 
few  observations  made  with  the  transit.  But  south  of  the  zenith  we  find  the  difference  to  assume 
a  well-marked  systematic  character,  the  positions  given  by  the  circle  being  uniformly  less  north  of 
the  equator  and  greater  south  of  it  by  amounts  too  great  to  be  the  result  of  accidental  errors. 

Such  a  result  would  follow  from  a  constant  error  in  the  collimation  of  either  instrument.  Me- 
ridian transits  are  referred  to  a  supposed  great  circle  passing  through  the  pole,  and  coinciding  with 


POSITIONS    OP    FUNDAMENTAL    STARS. 


27 


tin1  true  meridian  of  reference  on  the  circle  of  mean  declination  of  clock  stars.  If  this  supposed 
great  circle  is  really  a  small  one.it  will  cross  the  meridian  of  reference  on  the  circle  of  mean  declina- 
tion. To  express  the  fact  in  algebraic  form  it  is  easy  to  see  that  an  error  of  J  c  in  the  collimalion 
will,  by  its  direct  ell'ect  and  by  the  resulting  errors  in  the  polar  a/.imuth  and  the  clock  correction, 
give  rise  to  the  error 

J  c  (tan  <<  —  sec  »  —  tan  30  +  sec  <J0) 

in  «i  star  of  declination  ».  In  this  formula,  tan  <?„  and  sec  '50  represent  the  mean  values  of  tan  <>  and 
sec  ii  for  the  stars  on  which  the  clock  correction  depends.  If  we  suppose  <?„=  0,  the  error  will  become 

J  c  (1  +  tan  <5  —  sec  <5) . 
The  following  table  shows  the  value  of  the  coefficient  of  Sc  for  different  polar  distances. 


NPD 

Coefficient. 

o 

20 

+     0.82 

30 

+     0.73 

40 

4-     0.64 

50 

+     0.53 

00 

+     0.42 

70 

+     0.30 

80 

+     0.  1C 

90 

0.00 

100 

—    0.19 

110 

—    0.43 

120 

—    0.73 

130 

—     1.14 

To  ascertain  whether  there  is  any  systematic  difference  depending  upon  the  magnitude  of  the 
star,  we  collect  the  values  of  G  —  T  corresponding  to  those  thirteen  stars  the  magnitudes  of  which 
are  given  in  the  Kphcmcris  as  1  or  1.-,  and  those  twelve  which  are  of  or  below  the  fifth  magnitude. 
In  the  case  of  </  ('anis  Minoris,  C —  T  has  been  corrected  for  the  inequality  of  proper  motion  given 
by  Auwers  in  Ifo.  1373  of  the  Astronomische  Nachrichten : 


Bright  utare. 

Faint  stars. 

a  Tauri  -  . 

—  0.  012 

^  Geminor.    . 

—  0.  012 

ft  Orion  is  . 

+  0.007 

/c  C'ancri  . 

+  0.  0.12 

a  Canis  Mil.). 

—  0.  037 

i  Leonis  . 

+  O.dll 

£  ('anis.M.-ij. 

+  0.005 

T    1  .roll  is     . 

+  0.007 

a  Cauia  Mill. 

+  0.  004 

v  Leonis  . 

4-  0.005 

J)  Grmiiior 

—  0.008 

l>  OpbincM 

4-  0.023 

a  1  .1-1  in  is    . 

—  o.in:: 

'•  AqlliliU   . 

+  0.042 

a  Virninis 

—  0.  013 

T  Aquilitt  . 

0.000 

«   I!(K)tiM     . 

—  0.003 

//  Aquarii  . 

+  o.  o:«; 

ii  Scnrpii  . 

—  0.  001 

f  Aqiuirii  . 

—    (1.  (HIS 

•a  Lynn 

—  0.  015 

ft  Capricorni 

+  0.  022 

a  Aqililin  . 

—  0.006 

JT  Aquarii  . 

—  0.  014 

a  PiscisAus. 

+  O.u:1.- 

Mean  .     .     . 

—  0.  004 

Mean  .     .     . 

+  0.014 

The  difference  of  the  means,  08.018,  is  more  than  three  times  the  probable  mean  difference  of 
two  sets  of  values  of  0  —  T,  selected  at  random  from  the  list.  It  is,  therefore,  highly  probable  that 
there  is  a  real  difference  depending  on  the  magnitude  of  the  star,  the  faint  stars  being  observed  the 
later  with  the  circle.  Such  a  result  is  not  an  improbable  one.  The  spider  lines  of  the  circle  appear 
much  finer  than  those  of  the  transit,  while  the  illumination  of  the  field  is  fainter.  The  effect  of  the 
latter  cause  will  probably  be  to  make  an  observer  later  in  recording  a  transit.  If  all  stars  were 
recorded  later  by  the  same  amount,  their  right  ascensions  would  not  be  affected.  But  the  stray 
light  which  surrounds  a  bright  star  forms  a  bright  ground  for  the  dark  transit  wire  a  perceptible 
time  before  the  star  reaches  the  wire,  and  thus  tin-  approach  of  the  two  objects  is  distinctly  seen. 
As  we  take  fainter  stars  the  stray  light  disappears,  and  the  approach  is  less  distinctly  seen.  Thus, 
tin-  elfect  in  ipicstion  will  be  exaggerated  as  the  star  grows  fainter.  . 

Whatever  be  the  cause  of  this  etfeet,  \\e  ha\e  abundant  evidence  that  the  right   ascensions  of 


28 


POSITIONS    OF    FUNDAMENTAL    STARS. 


faint  objects  given  by  different  authorities  sometimes  exhibit  discrepancies  which  can  hardly  depend 
on  anything  but  the  magnitude.  A  striking  instance  of  this  is  given  by  the  planet  Neptune.  In 
the  Washington  Observations  for  1806,  p.  400,  is  given  a  column  of  corrections  to  the  Ephemeris  of 
Neptune,  found  in  the  appendix  to  the  American  Ephemeris  for  18(59,  from  which  it  appears  that 
the  mean  correction  to  that  ephemeris  given  by  the  observations  with  the  transit  circle  is  +  0N.09U. 
But  a  similar  comparison  with  the  Greenwich  observations  for  18(5(!  indicates  no  correction  what- 
ever. In  18(57  a  brighter  illumination  was  given  the  Held  of  the  Washington,  circle,  and  the  dis- 
crepancy was  reduced  to  Os.03(). 

These  circumstances  strengthen  the  view  already  presented  that  an  observer  may  observe 
transits  at  night  systematically  later  than  in  the  day. 

EIGHT  ASCENSIONS  OF  POLARIS. 

The  right  ascensions  of  Polaris  demand  a  separate  investigation,  on  account  of  the  different 
character  of  the  data  on  which  they  depend,  and  the  existence  of  well-marked  personal  differences 
in  the  results. 

In  the  following  collection  of  right  ascensions  all  results  are  omitted  except  those  of  consecu- 
tive transits  by  the  saifie  observer.  As  a  single  transit  gives  only  an  equation  of  condition  between 
the  azimuth  and  the  right  ascension,  a  pair  of  opposite  transits  is  considered  as  giving  only  a  single, 
result  for  right  ascension.  As  the  coefficients  of  the  azimuth  in  the  equations  are  nearly  equal,  and 
of  opposite  signs,  we  may  take  as  this  single  result  the  mean  of  the  separate  results  of  the  two  tran- 
sits reduced  with  any  value  of  the  azimuth  reasonably  near  the  truth. 

Classifying  the  right  ascensions  according  to  the  observer,  we  have  the  corrections  to  the  right 
ascensions  of  the  American  Ephemeris  given  on  the  next  page.  The  third  column  gives  the  correc- 
tions as  they  result  immediately  from  the  observations.  Large  personal  differences  in  the  results 
being  evident,  the  mean  result  from  the  work  of  each  observer  during  each  year  is  taken  and  is 
given  at  the  end  of  the  columns.  It  appears  from  this  that  there  is  a  difference  of  more  than,  two 
seconds  between  the  result  of  Professor  Hall's  observations  and  that  of  Mr.  Thirion's.  Eeduced  to 
arc  of  a  great  circle,  this  difference  amounts  to  0".82,  or  08.054  in  time. 

It  will  also  be  seen  that  each  of  the  three  observers  who  observed  throughout  both  years  gives 
a  smaller  correction  in  1867  than  in  18C6,  the  differences  being  as  follows: 


This  change  may  be  partly  due  to  the  different  position  of  the  instrument  during  the  second  year. 

For  the  purpose  of  reducing  the  results  to  a  common  standard,  the  general  mean  is  taken,  and 
found  to  be  appreciably  +  18.0.  The  systematic  correction  to  reduce  the  results  of  each  observer  to 
this  standard  is  applied  to  the  results  in  the  third  column  to  obtain  those  in  the  fourth.  It  may  be 
a  question  whether  this  correction  should  be  considered  the  same  for  both  years,  or  whether  the 
results  for  each  year  should  be  taken  and  applied  separately.  A  middle  course  has  been  adopted  by 
applying  the  following  corrections : 


01  is. 

18«>. 

18G7. 

8. 

X. 

N. 

0.0 

+  0.4 

II. 

+  1.0 

+  1.0 

i;. 

—  0.1 

T. 

—  1.4 

-1.1 

POSITIONS   OF    FUNDAMKNTAL    STARS. 


29 


Thus,  the  fourth  column  Drives  the  results  as  they  would  have  been  had  all  the  observations 

made  b\  a  single  mean  observer. 

KllIlIT   ASCMNSIONS  or   PHI.  \1!1S   HKIHVKn   KUdM   DOriH.K  TRANSITS  ]!V  T1IK  SKVKIi.U,  OI'.SKKVI- I;S. 


_ 

Cc.rriTt  n  In 
Am.  K|ilirm. 

j[    = 

- 

ti 

Corrcct'n  If. 
Am.  Ephcin. 

ji 

Date. 

O 

Correct'n  to 
Am.  Eiilicin. 

Reduced  cor- 
rection. 

Date. 

Observer. 

Correct'n  to 
Am.  Ephem. 

If 

1866. 

1. 

,. 

1866. 

,. 

«. 

1867. 

.. 

s. 

•1867. 

I. 

#. 

.h.u.         4 

R. 

+     2.0 

+     1.9 

July      11 

T. 

+     14 

ao 

Jau.        7 

K. 

—    1.2 

—    0.8 

Sept.    IB 

N. 

+     0.6 

+     1.0 

5 

11. 

+     1-4 

+     2.4 

13 

H. 

0.0 

+     1.0 

11 

H. 

+     0.4 

+     1.4 

23 

11. 

0.0 

+     1.0 

8 

H. 

—    2.5 

—    1.5 

14 

T. 

+     1.4 

o.o 

17 

X. 

+    0.8 

+     1.2 

24 

T. 

+     1.7 

+     0.6 

9 

R. 

+     0.3 

+   a  2 

26 

X. 

+    0.8 

+    0.8 

23 

T. 

+    0.3 

—    0.8 

27 

H. 

+     1.3 

-(      2.3 

Feb.        1 

R. 

—    0.1 

—    0.2 

August  3 

T. 

+    0.6 

-    0.8 

84 

X. 

—    0.5 

—    0.1 

28 

T. 

+     4.4 

+     3.3 

3 

T. 

+     2.3 

+     0.9 

4 

R. 

+     1-7 

+     1-6 

28 

X. 

0.0 

+     0.4 

30 

X. 

+     2.5 

+     2.9 

:, 

R. 

+     1.0 

+     0.9 

r, 

N. 

+     1.2 

+     1.2 

29 

H. 

0.0 

+     1.0 

Oct.         1 

H. 

—    0.8 

+     0.2 

6 

H. 

—    0.4 

+     0.6 

9 

R. 

+     1.6 

+     1.5 

31 

N. 

+     2.4 

+    3.8 

7 

X. 

0.0 

+     0.4 

15 

R. 

—    2.7 

—    2.8 

10 

H. 

—    0.4 

+    0.6 

Feb.       5 

H. 

—     1.2 

—    0.2 

8 

H. 

—    0.4 

+     0.6 

16 

H. 

0.0 

+     1.0 

15 

T. 

+     1.6 

+    0.8 

6 

T. 

+     2.5 

+     1.4 

12 

T. 

+     3.1 

+     1.0 

20 

R. 

—    2.2 

—    2.3 

16 

R. 

—    0.1 

-0.2 

7 

N. 

—    0.7 

—    0.3 

14 

H. 

+     1.5 

+  •2.5 

•Jl 

T. 

+     3.4 

+     2.0 

17 

H. 

—    0.8 

+    0.2 

26 

H. 

-1.7 

—    0.7 

15 

A. 

+     1.5 

• 

22 

R. 

—    1.0 

1.1 

1- 

T. 

+     4.0 

+    3.6 

27 

T. 

+     0.4 

—    0.7 

16 

T. 

+     2.5 

+     1.4 

March    5 

II. 

—    0.4 

+     0.6 

22 

T. 

+     3.4 

+    8.0 

March  18 

N. 

+     1.5 

+     1.9 

18 

A. 

+     1.7 

8 

X. 

r     1.2 

+     1.2 

Sept.      5 

T. 

+     3.2 

+     1.8 

28 

N. 

+•   0.5 

+     0.  9 

19 

T. 

+     2.0 

+     0.9 

10 

T. 

+     3.7 

+     2.3 

8 

T. 

—    1.0 

—    2.4 

29 

H. 

-0.6 

+     0.4 

23 

H. 

—    2.2 

—    1.2 

26 

X. 

—    1.2 

—    1.2 

12 

T. 

+     0.7 

-0.7 

30 

T. 

+     2.7 

+     1.6 

24 

A. 

+     0.4 

. 

27 

R. 

+    2.0 

+    1.9 

14 

T. 

+     1.0 

—    0.4 

April      1 

X. 

—    0.6 

—    0.2 

M 

6. 

—    1.2 

—    0.2 

30 

N. 

—    0.9 

—    0.9 

15 

R. 

f     2.0 

+     1.9 

2 

H. 

—    1.1 

-    0,1 

Xov.      5 

A. 

+     0.3 

April      5 

R. 

+    0.8 

+    0.7 

17 

T. 

+     1.8 

+     0.4 

3 

T. 

+    2.2 

+     1.1 

6 

T. 

+     2.4 

+-     1.3 

11 

T. 

+     3.3 

+     1.9 

22 

N. 

+     2.2 

+     2.2 

5 

H. 

—    0.8 

+    .0.2 

8 

A. 

+     2.2 

1!' 

X. 

+     1.4 

+    1.4 

27 

K. 

+     2.6 

1      2.6 

6 

T. 

+     8.2 

+     LI 

12 

A. 

\-     0.1 

20 

R. 

+     0.4 

+     0.3 

28 

R. 

+     0.8 

+     0.7 

13 

T. 

(-  1.  4:) 

(—  2.5) 

18 

H, 

—    0.1 

+    0.9 

May        3 

R. 

+     1.3 

+     1.2 

Oct.         4 

R. 

+     2.4 

+     2.3 

17 

T. 

+     1.8 

+     0.7 

19 

A. 

+     1.6 

. 

4 

H. 

—    0.8 

+    0.2 

5 

H. 

+    0.6 

+     0.4 

18 

H. 

+     1.0 

+     2.0 

20 

T. 

+     0.4 

—    0.7 

5 
7 
14 
15 
19 
21 

T. 
X. 
N. 
R. 
T. 
N. 

+    1.7 

+    0.3 
—    0.2 

+     1.8 
+     2.2 
+     0.8 
—    2.0 

6 
8 
15 
16 
17 
18 

X. 
X. 
X. 
R. 
H. 
R. 

+     1.2 
+    3.3 
+     M 
+    3.0 
+     1.3 
+    8.0 

+     1.2 
+     3.3 

+     M 

+    8.3 
+     1.9 

96 
May       9 
11 
14 
17 
18 

H. 

N. 
T. 
T. 
H. 
T. 

+     2.9 
+     1.2 
+     3.7 
+     0.1 
—    0.4 
+     1-2 

+     3.9 
+     1.6 
+     2.6 
—     1.0 
+     0.6 
+     0.1 

Dec.        9 
Mean.    . 

H. 

N. 
H. 
T. 
A. 

+     1.3 

+     2.3 

+     1.8 
+     2.3 
+    2.2 
—    2.0 

+     0.39 
—    0.10 
+     2.00 
+     1.  11 

22 

H. 

—    0.1 

+     0.9 

19 

H. 

+     1.0 

+    3.0 

23 

N. 

+     0.1 

+     0.5 

23 

T. 

+    3.6 

+     2.2 

20 

X. 

+    2.6 

+     2.6 

24 

H. 

0.0 

+     1.0 

24 

N. 

+     1-1 

+     1.1 

23 

R. 

+     1.4 

+     1.3 

27 

N. 

—    0.8 

—    0.4 

• 

H. 

+     1.0 

+     2.0 

27 

X. 

+     2.2 

+     2.2 

31 

H. 

+     0.4 

+     1-4 

• 

X. 

+    0.1 

+     0.1 

31 

H. 

—    0.2 

+    0.8 

June       1 

N. 

+     0.6 

+     1.0 

30 

T. 

+    5.0 

+     3.6 

Xov.       1 

R. 

Kl 

+    0.4 

4 

T. 

+     2.8 

+     1-7 

31 

N. 

+    8.4 

+     2.4 

2 

II. 

—    0.9 

+    0.1 

6 

X. 

+     0.7 

+     1.1 

June      4 

X. 

+    1.6 

+     1.6 

5 

X. 

+    3.4 

+    3.4 

10 

N. 

+     1.2 

+     1.6 

6 

II. 

+    1.2 

+     2.2 

6 

R. 

+    2.3 

+    8.9 

11 

T. 

+     2.6 

+     1.5 

7 

X. 

—    0.2 

—    0.2 

7 

T. 

+    5.6 

+     4.2 

15 

T. 

+     0.8 

—    0.3 

11 

N. 

+    1.8 

+     L8 

8 

R. 

—    0.8 

—    0.9 

21 

H. 

—    0.8 

+    0.2 

13 

JI. 

+    1.8 

+    3.8 

9 

H. 

+     1-2 

+    2.2 

July      24 

T. 

+    2.4 

+     1.3 

15 

H. 

—    0.3 

+    0.7 

12 

X. 

+    4.1 

+    4.1 

27 

T. 

+    2.0 

+     0.9 

n 

R. 

+    0.6 

+    0.5 

13 

R. 

+    3.8 

+     17 

31 

T. 

+    2.0 

+     0.9 

20 

T. 

+    3.8 

+     1.8 

• 

R. 

+     4.2 

+    4.1 

Ang.     23 

H. 

—    1.4 

—    0.4 

SI 

X. 

+     1.0 

+     1.0 

21 

T. 

+    3.1 

I-     0.7 

Sept.       4 

T. 

+    2.7 

+     1.6 

'-T. 

N. 

+     1.0 

+     1.0 

M 

T. 

+    8.8 

1      1.4 

5 

H. 

+     0.6 

+     1.6 

2fi 
30 
.Inly        5 
6 

7 

R. 
H. 
X. 
R. 
H- 

f     2.0 
0.0 
—    0.3 
+     1.4 
+     0.4 

+     1.9 
1.0 
—    0,3 

i.:i 
+     1.4 

Mora.    - 

X. 

X. 
II. 
R. 
T. 

-0.4 

-0.4 

6 

n 

12 
13 

18 

X. 
T. 
X. 
II. 
T. 

+    0.5 
+     1.5 
—    1.0 

M 

+     2.7 

+     0.9 
+     0.4 
—    0.6 
+     1.9 
+     1.6 

+     1.18 
+     0.14 
+     1.13 
+    9.48 

POSITIONS    OF    FUNDAMENTAL    STARS. 


The  principal  object  of  this  fourth  column  is  to  furnish  the  means  of  detecting  any  diurnal 
change  in  the  pointing  of  the  instrument  near  the  pole.  The  old  transit  instrument  is  known  to  be 
affected  with  such  a  change.*  The  existence  of  this  state  of  things  will  be  manifested  by  a  corre- 
sponding inequality  in  the  time  of  transit  of  Polaris,  depending  upon  the  time  of  d;iy  at  which  the 
transit  takes  place ;  there  will,  therefore,  be  a  corresponding  annual  inequality  in  the  right  ascen- 
sions of  this  star  deduced  from  observations.  Let  us  put  n  for  the  error  of  pointing  of  the  instru- 
ment near  the  pole,  a  west  azimuth  being  considered  positive.  Put,  also,  w,,  and  «„  for  the  values 
of  n  at  upper  and  lower  transits,  respectively ;  then  the  upper  transit  will  be  too  late  by 

nu  sec  <5; 
and  the  lower  transit  by 

—  na  sec  S. 

The  right  ascension,  deduced  from  the  transits,  will  therefore  be  too  late  by 

i  (nu  —  n*)  sec  S. 

If  the  pointing  of  the  instrument  undergoes  a  periodic  diurnal  change,  we  shall  have 

n  —  a  sin  D  +  b  cos  D, 

a  and  b  being  constants,  and  D  being  the  time  of  day  expressed  in  arc.  Put  Du  for  the  time  of  day 
at  which  upper  transit  takes  place ;  the  lower  transit  will  then  take  place  at  Du  +  ll"1,  and  we  shall 
have 

MU  =      a  sin  Du  +  b  cos  Du ; 

na  =  —  a  sin  Dn  —  b  cos  Du  ; 

and  the  error  of  right  ascension  will  be 

da  =  (a  sin  Du  +  b  cos  Du)  sec  <5. 

About  April  7  of  each  year  the  upper  transit  takes  place  at  noon,  and  we  then  have  Du  =  0 
and  we  have  at  any  time  thereafter 

Dn  =  — y, 

y  being  the  fraction  of  a  year  counted  from  April  7,  and  expressed  in  arc.  Sec  S  being  about  40.7, 
we  have 

8  a  =  40.7  ( —  a  sin  y  +  b  cos  y). 

We  shall  consider  the  fourth  column  of  the  preceding  table  as  giving  a  series  of  values  of  3  a 
plus  an  unknown  constant,  extending  through  a  period  of  two  years.  Combining  the  correspond- 
ing months,  and  taking  the  mean  value  of  3  a  +  c  for  each  month,  we  have,  with  the  omission  of 
December — 


Month. 

Mean  and  equation  of  condition. 

No.  of  obs. 

Wt. 

January- 

s. 
+  0.  68  =  c  +  0.  99  X  40.  7  a  +  0.  14  X  40.  7  b 

12 

1 

February     . 

—  0.  11  =  c  +  0.  79                    +0.  62 

14 

1 

March 

+  0.  87  =  c  +  0.  37                    +0.  93 

10 

1 

April 

'+  1.  08  =  o  —  0.  14                    +  0.  99 

12 

1 

May  -     .     . 

+  0.  96  =  c  —  0.  G2                   +  0.  79 

24 

2 

June  . 

+  0.  19  =  c  —  0.  93                    +  0.  37 

19 

2 

July  . 

-f  0.  73  =  c  —  0.  99                   —  0.  14 

10 

1 

August   - 

+  0.  77  =  c  —  0.  79                    —  0.  62 

11 

1 

September  . 

+  1.12  =  c  —  0.37                    —0.93 

22 

2 

October..     . 

+  1.35  =  c  +  0.14                    —0.99 

22 

2 

November    . 

+  1.70  =  0  +  0.62                    —0.79 

17 

2 

Washington  Observations  for  1862,  pp.  xv.  x\  i. 


POSITIONS    OF    FUNDAMENTAL    STARS.  31 

The  solution  of  those  equations  gives 


40.7  a  =   -<U»7 
10.7  b  =  —  0.29 

// 

a  =  —  0.03 
b  =  —  0.11 

If  we  consider  those  minute  values  of  a  and  b  as  due  to  parallax  and  error  in  the  constant  of 
aberration,  \vo  shall  lind  a  value  of  the  parallax  sensibly  equal  to  —  «,  and  a  correction  to  the  con- 
stant of  aberration  sensibly  equal  to  —  b;  we  shall,  therefore,  have 

// 
Parallax  of  Polaris  ...........     0.03 

Constant  of  aberration  ..........  20.55 

In  other  words,  the  apparent  annual  inequality  in  the  observed  mean  right  ascension  of  Polaris 
may  be  accounted  for  indifferently  by  a  diurual  inequality  in  the  pointing  of  the  instrument,  or  by 
parallax  and  error  of  aberration  constant. 


CHAPTER    II. 
POLAR  DISTANCES  OF  FUNDAMENTAL  STAES. 

If  the  pole  were  a  visible  point  in  the  heavens,  the  polar  distance  of  an  object  would  be  deter- 
mined in  the  following  way :  We  should  point  the  telescope  upon  the  pole,  and  determine  the  circle 
reading  for  this  pointing  exactly  as  in  the  case  of  a  star.  This  circle  reading,  corrected  for  all 
known  errors  pertaining  to  the  instrument,  and  for  refraction,  we  shall  represent  by  Cp.  The  tele- 
scope is  then  pointed  on  the  star.  The  circle  reading,  corrected  for  the  effect  of  all  known  sources 
of  error,  will  be  called  C,.  We  shall  then  have 

N.  P.  D.  =  C.  — Cp. 

A  separate  and  independent  result  may  be  obtained  by  pointing  upon  the  images  of  the  pole 
and  star  reflected  from  the  surface  of  quicksilver.  If  we  represent  the  corrected  circle  readings  by 
C'.  and  C'p,  the  result  will  be 

N.  P.  D.  =  C'P  — C'.. 

If  we  find  in  this  way,  C.  —  Cp  =  C'p  —  C'.  or,  C.  +  C'.  =  Cp  +  C'p,  the  results  will  be  accord- 
ant ;  otherwise  there  will  be  discordance. 

We  see  that  neither  latitude  nor  zenith  point  enters  into  the  expression  for  either  the  direct  or 
reflected  polar  distance. 

The  pole  not  being  a  visible  point,  the  direct  application  of  this  method  is  not  practicable.  Our 
present  object  is  to  deduce,  from  the  usual  system  of  observations,  the  result  which  would  follow  if 
the  pole  were  a  visible  point  and  distances  were  measured  from  it  in  the  way  described. 


In  the  above  diagram  let  S  N  represent  the  horizon,  P  the  pole,  C,  D,  and  E,  the  directions  of 
three  stars  at  culmination ;  and  Ci  and  Dj  the  positions  of  C  and  D  at  lower  culmination.    Let  the 
5 


34  POSITIONS    OP    FUNDAMENTAL    STARS. 

accented  letters  represent  the  directions  of  the  same  objects  as  seen  by  reflection  from  a  truly  hori- 
zontal surface.  For  the  purposes  of  analysis  let  us  represent  the  circle  readings  corresponding  to 
each  direction  by  the  letter  marking  the  direction,  and  the  polar  distances  by  the  letters  inclosed  in 
parentheses.  Then, 

For  the  polar  distance  of  the  star  E,  we  shall  have  the  two  values  .     .     .      E  —  P  ; 

P'  —  E'. 
For  (D)  we  shall  have  the  three  values  ...........  D  —  P  ; 

P-D15 

P'—  D'. 
For  (C)  we  may  have  the  four  values  ............  C  —  P; 

P-C,; 

P'  —  C'; 

C'i—  P'  . 

The  agreement  of  these  polar  distances  would  furnish  a  check  upon  the  accuracy  of  the 
measures. 

If  the  value  of  P  were  invariable,  we  should  put 


which  would  still  leave  us  with  two  independent  values  of  (E)  and  (D),  and  three  of  (C),  with  an 
equation  of  condition  between  (C)  and  (D). 

Since  C  and  Cj  cannot  be  determined  simultaneously,  we  shall  suppose  an  invariable  point  O, 
the  circle  reading  corresponding  to  which  can  be  determined  at  any  time.  Such  a  point  is  the 
"  zenith  point  ;"  but  for  our  present  purposes  it  is  quite  indifferent  whether  it  be  in  the  true  zenith 
of  the  place  or  not.  Our  data,  therefore,  consist  of  a  series  of  values  of  E',  E,  D,  &c.,  determined 
irregularly  on  various  dates,  with  a  separate  value  of  O  for  each.  We  shall  suppose  each  determi- 
nation reduced  to  a  mean  epoch,  so  that  the  reduced  values  of  E  —  O,  O  —  D,  &c.,  are  invariable, 
errors  of  observation  excepted.  We  then  have 

O  —  P  =  £{O-C  +  O  —  Ci}  =  £{O  —  D  +  O  —  D,}. 
The  second  equation  is  equivalent  to 


so  that  the  agreement  or  disagreement  between  the  values  of  O  —  P,  or  of  the  colatitudes,  derived 
from  stars  of  different  polar  distances,  is  indicative  of  a  corresponding  agreement  or  disagreement 
between  measures  made  above  and  below  the  pole. 
In  the  same  way  we  have 

P'  —  O  =  J{C'  —  O  +  C't  —  O}. 

Commonly,  however,  the  number  of  determinations  of  the  class  C'j,  or  of  reflection  observa- 
tions below  the  pole,  is  too  small  to  determine  P'.  But  (C)  and  (D)  being  determined  from  the 
direct  observations,  we  have  several  independent  values  of  P'  —  O  from  the  equations 

P'—  O  =  C'  —  O+(C)  =  D'  —  O+(D),  &c. 

If  these  different  values  agree,  it  shows  that  the  measured  arc  C'  D'  is  equal  to  the  measured 
arc  C  D,  or  that  the  direct  and  reflection  polar  distances  agree. 

Let  us  now  represent  the  mean  value  of  O  —  P  thus  obtained  by  p,  and  that  of  P'  —  O  by  <p'  ; 
let  us  also  put  Z  >=  E  —  O  :  Z'  —  O  —  E'. 


POSITIONS    OF    FUNDAMENTAL    STARS.  35 

"We  then  have 


These  values  of  (E)  and  (E')  will  be  the  same  as  if  they  were  measured  from  a  visible  pole  in  the 
heavens,  corresponding  to  the  mean  of  the  stars  by  which  the  value  of  <p  was  deduced. 

If  we  represent  by  <  the  inclination  of  the  direction  O  toward  the  north,  we  shall  have 

O  —  D  +  O  —  D'  =  180°  —  2i. 

Each  star  observed  both  directly  and  by  reflection,  will  give  an  independent  value  of  t,  and 
the  agreement  or  disagreement  between  the  values  oft  thus  obtained  will  indicate  a  corresponding 
agreement  between  the  distances  of  the  stars  deduced  from  direct  and  reflection  observations,  since 

O  —  C  +  O'  —  C'  =  O  —  E  +  O'  —  E' 
is  equivalent  to 

E-C=E'  —  C'. 

Having  thus  explained  a  rigorous  system  of  deducing  several  independent  sets  of  polar  dis- 
tances from  observations  as  usually  made,  let  us  apply  the  principles  of  this  system  to  the  obser- 
vations and  reductions  under  discussion.  The  published  volumes  of  Washington  Observations  for 
the  years  ISGtf  and  1867  give  us  a  system  of  circle  measures  made  and  reduced  in  the  following  man- 
ner: Corresponding  to  O  was  a  "zenith  point"  determined  from  observations  of  the  collimators  and 
nadir  point.  Were  the  determinations  free  from  all  source  of  error,  this  zenith  point  would  be  the 
true  one,  and  we  should  have  i  =  0  ;  but  as  the  determination  may  be  liable  to  systematic  errors, 
we  shall  regard  i  as  an  unknown  quantity  to  be  determined.  The  observations  were  further  reduced 
by  supposing 

o    '       " 

O  —  P  =  y>  =    61  6  21.20  ; 
6  21.20. 


These  quantities  being  applied  to  the  measured  values  of  E  —  O  =  Z  and  O  —  E'  =  Z',  values 
of  the  reduced  polar  distances  of  the  stars  were  thus  obtained.  Let  us  represent  these  assumed 
values  of  y  and  ?'  by  p0  and  f'0,  the  true  values  not  being  known.  Let  us  also  put 


3y  and  H<f'  being  the  unknown  quantities  to  be  determined.    The  polar  distances  actually  found  by 
the  reductions  given  in  the  published  volumes,  are 

Z  -f  <FC  (from  direct  observations.) 
Z'  4-  f'o  (from  reflection  observations.) 

It  will  be  remembered  that  in  the  preliminary  reductions  given  in  the  volumes  of  observations 
under  the  title,  Observations  with  the  Transit  Circle,  no  corrections  have  been  applied  for  flexure  or 
error  of  division,  it  being  thought  most  convenient  to  apply  the  same  once  for  all  to  the  mean  results. 

In  what  follows  we  shall  suppose  Z  and  Z'  to  have  received  these  corrections.    From  the  equations 

Z  =  E  —  O  Z'  =  O  —  E' 


O  —  E  +  O  —  E'  =  1800  _  2  1 
we  obtain,  first, 

Z  —  Z'  =  E  —  O+E'  —  O  =  180°  +  2t, 

and  next, 


36 


POSITIONS    OF    FUNDAMENTAL    STARS. 


or,  the  value  of  i,  deduced  from  the  observations  of  any  star,  is  simply  the  discordance  between  the 
direct  and  reflection  polar  distances  of  that  star  found  by  the  preliminary  reductions.  This  result 
will  be  made  evident  by  considering  that,  proceeding  as  we  are,  upon  the  supposition  that  all  meas- 
ures of  arcs  are  correctly  made,  or  that  all  circle  readings  are  affected  with  only  a  common  error  in 
the  zero  point,  the  only  source  of  discordance  will  arise  from  the  inclination  of  the  adopted  zenith 
line,  and  this  inclination  will  produce  a  discordance  of  double  its  amount  in  the  zenith  distances 
derived  by  the  two  methods. 

In  the  published  volume,  the  mean  values  of  the  discordance  in  question  is  given  for  every  10° 
of  Z.  D.    The  following  are  the  resulting  values  of  i : 


Z.  D. 

Value  of  i. 

1866. 

1867. 

o 

// 

// 

310 

+  0.78 

+  0.44 

321 

+  0.96 

+  0.54 

330 

+  0.90 

-f  0.44 

340 

4-  1.38 

+  0.  36 

350 

+  1.01 

+  0.48 

10 

-f  0.54 

—  0.09 

20 

+  0.44 

-  0.14 

30 

+  0.49 

—  0.13 

40 

+  0.70 

-  0.24 

48 

+  0.48 

—  0.16 

It  has  been  shown  that  an  agreement  or  disagreement  between  the  values  of  i,  obtained  from 
different  stars,  indicates  a  corresponding  agreement  or  disagreement  between  the  arcs  of  polar  dis- 
tance included  between  those  stars  as  measured  directly  and  by  reflection,  the  disagreement  being 
double  the  difference  between  the  values  of  i.  It  appears,  therefore,  that  the  measures  in  question 
exhibit  the  following  peculiarities  :  During  the  year  1866,  as  we  measure  from  the  pole  toward  the 
southern  horizon,  we  find,  as  we  approach  the  zenith,  that  the  reflected  arcs  are  a  little  less  than  those 
measured  directly,  the  difference  at  30°  of  N.  P.  D.  being  more  than  1".  But,  as  we  pass  the  zenith, 
there  is  a  sudden  increase  in  the  reflected  measure,  which  remains  sensibly  constant  as  far  as  the 
reflected  arcs  extend.  During  the  year  1867  there  is  no  sensible  discordance,  except  a  sudden 
extension  of  the  reflected  measure  by  1".2  near  the  zenith,  such  that  all  arcs  which  do  not  pass 
over  the  zenith  agree,  while  those  which  pass  over  it  exhibit  the  difference  in  question. 

Were  reflection  observations  extended  to  the  horizon,  the  values  of  <p  and  </>'  could  be  deter- 
mined independently.  As  they  cannot  be  so  extended,  we  have  to  employ  the  auxiliary  i  in  the 
expressions 

y  =  —  i(Z  +Z,); 


/,  <<>  —  p'  =  180°  —  2i. 

Since  ?'  is  used  only  to  fix  the  position  of  the  reflected  pole,  the  value  of  i  to  be  employed  should 
be  derived  solely  from  those  stars  which  may  be  observed  on  both  sides  of  the  pole.  Actually  it  has 
been  derived  from  the  reflection  observations  north  of  the  zenith,  which  leads  to  nearly  the  same 
result.  The  values  of  i  employed  are,  therefore, 

for  1866,  i  =  +  0".!)(i 
1867,  i  =  +  0".45 

The  further  investigation  of  y  is  substantially  the  same  with  that  for  the  correction  of  latitude 


POSITIONS    OF    FUNDAMENTAL    STARS. 


already  {riven,  with   the  differenee  thai    i  has  been  applied  to  the  provisional  polar  distances  in 
advance.     The  results  are  as  follows: 

Had  the  pole  been  a  visible  point  in  the  heavens,  the  pointing  on  which  corresponded  to  the 
mean  pointing  on  cm-unipolar  stars  above  and  below  the  pole,  we  should  have  found  for  the 
measured  arc,  from  that  point  to  the  adopted  zenith  point  derived  from  collimator  observations, 

o    '       "  " 

in  1866,  <p  =  51  6  20.74  ;  Sy  =  —  0.46  ; 
1867,  f  =  51  6  21.25  ;  8<f  =  +  0.05  . 

And  for  the  arc  between  the  adopted  zenith  point  and  the  reflected  pole, 

o     i       n  n 

in  1866,  y.'  =  231  6  22.66  ;  Sy'  =  +  1.46  ; 
1867,  <f'  =231  6  22.15  ;  8<p'  =  +  0.95  . 

It  will  be  seen  that  the  values  of  <p  -(-  <?',  or  the  measured  arcs  between  the  direct  and  reflected 
poles,  agree  perfectly  in  the  two  years ;  this  agreement  has,  however,  been  brought  about  by  first 
adopting  the  value  zero  for  the  cosine  flexure  of  the  telescope,*  which  made  the  difference  very 
small,  and  then  combining  the  results  of  the  two  years  on  the  supposition  that  the  two  measures 
were  equal. 

Applying  the  above  values  of  <p  and  y>'  to  the  observed  zenith  distances,  we  shall  obtain  the 
results  already  set  forth,  that  the  polar  distances  north  of  the  zenith  exhibit  no  great  discordances, 
whether  measured  above  or  below  the  pole,  directly  or  by  reflection,  while  in  arcs  which  extend 
south  of  the  zenith,  the  reflected  polar  distances  are  constantly  greater  by  a  nearly  constant 
amount. 

The  corrections  which  have  to  be  applied  to  the  positions  obtained  by  the  preliminary  reduc- 
tions to  reduce  them  to  actual  measures  from  the  pole  to  the  stars  are  simply,  flexure  +  division 
+  S<forS<f'.  The  corrections  for  flexure  and  division  are  discussed  in  the  introductions  to  the 
several  volumes  of  Observations ;  6<p  and  S<p'  have  just  been  given.  As  already  indicated,  we  shall 
find,  on  applying  these  corrections,  that  the  reflection  measures  which  extend  south  of  the  zenith 
are  greater  than  the  direct  ones  by  about  1".  As  a  last  correction  to  reduce  both  measures  to  a 
uniform  system,  we  shall  divide  this  discrepancy  between  the  two  classes  of  observations.  More- 
over, instead  of  supposing  the  change  to  take  place  suddenly  at  the  zenith,  it  will  be  spread  over  a 
space  of  5°  on  each  side.  The  concluded  corrections  thus  obtained  are  the  same  as  those  finally 
given  in  the  introductions  to  the  two  volumes  of  Observations.  Applying  them  to  the  preliminary 
means,  we  have  the  following  corrections  to  the  north  polar  distances  of  the  American  Kphemeris, 
with  the  number  of  standard  independent  observations  to  which  the  actual  observations  made  are 
considered  equivalent : 

*  Washington  Observations  for  1866,  pp.  xxiv,  xxv,  and  for  1867,  p.  xx. 


38 


POSITIONS    OB'    FUNDAMENTAL    STARS. 


CORRECTIONS  TO  THE  NORTH  POLAR  DISTANCES  OF  THE  STARS  OF  THB  AMERICAN  EPHEMERIS,  DEDUCED  FROM 

OBSERVATIONS  WITH  THE  TRANSIT  CIRC  I. K. 


Star.' 

1866. 

1867. 

Mean. 

Star. 

1866. 

1867. 

Mean. 

D. 

R. 

D. 

R. 

D. 

E. 

D. 

R. 

a    Andromeda?   . 

+      1.4, 

+     0.9, 

+      1.6. 

+    1.3, 

+  1.52 

*    Cancri  .... 

+     1.1, 

" 

+     0.  2S 

» 

+  0.46 

y    Pegasi  .... 

+     0.  5, 

+      1.1. 

+   2.0, 

+  1.03 

1     (H)  Draconis 

+      1.  Oj 

+    0.4, 

+  0.70 

a    Cassiopero  .     . 

+     0.7, 

-     0.2, 

+     0.9, 

+    0.4, 

+  0.43 

1    (H)  Drac.,  S.  P.  . 

-     0.74 

—  0.70 

a    Cassiopera,  S.  P.  . 

—     0.2 

—  0.20 

a    Hydra  .... 

+      1.44 

+     0.8, 

+    i.  o. 

+   2.03 

+  1.27 

ft    Ceti  

-     0.4, 

-     0.2, 

—  0.28 

0    Ursae  Majoris     . 

-     0.5, 

—  0.50 

21  CassiopeaB      .     . 

-     2.1, 

-     0.5, 

-  2.0, 

—  1.78 

t     Leonis  .... 

+     0.54 

+     0.8, 

+    0.4, 

+  0.64 

21  Cassiopeae,  S.  P.  . 

+    2.  7, 

+      1.6, 

+  1.91 

p    Leonis  .... 

-     0.1, 

+     0.9, 

+      0.  S, 

+  0.59 

t    Piscium     .     . 

+     0.5, 

+      1.2, 

+  0.88 

a    Leonis  .... 

+    i.o. 

-     0.1, 

+      1.3, 

+    0.4, 

+  0.92 

Polaris  .... 

—     0.  34, 

+      0.  264 

+      0.26,, 

+    0.356 

+  0.13 

y    Leonis  .... 

-     0.  34 

0.0, 

+      0.8, 

+    1.0, 

+  0.42 

Polaris,  S.  P.  .     . 

—     0.06, 

—     0.  464 

-     0.04,, 

+    0.03, 

—  0.09 

9    (H)  Draco.      .     . 

—     0.8, 

-     1.2, 

-     1.1, 

—   1.9, 

—  1.22 

9    Ceti      .... 

+      0.24 

+      1.6, 

+      0.  2, 

+  0.34 

9    (H)  Draco.,  S.P.  . 

K     L44 

+  1.40 

A  Cassiopese,  S.  P.  . 

+      1.0, 

+  1.00 

p    Leonis  .... 

0.0, 

0.0, 

0.00 

n    Piscium    .     . 

+      0.4, 

+     0.  9, 

+      1.0, 

+  0.77 

I     Leouis  .... 

0.04 

-     0.3, 

+      0.74 

0.0, 

+  0.21 

a    Piscium    .     .     . 

-     0.  24 

+     0.  7, 

+      1.2, 

+  0.69 

a    Ursse  Majoris 

+     0.6, 

-     1.5, 

-     0.3, 

-   1.1. 

—  0.63 

0   Arietis      .     .     . 

+      0.  46 

+      1.6, 

+  1.09 

i    Leonis  .... 

+     0.3, 

+     0.8, 

+      0.9, 

+  0.68 

50  Cassiopeae      .     . 

-     1.7, 

0.0, 

0.0, 

—  0.68 

i    Crateris     .     .     . 

0.0, 

-     2.7, 

0.  06 

—  0.30 

50  Cassiopere,  S.  P.  . 

-     0.4, 

+      0.  6, 

+  0.20 

r    Leonis  .... 

+      1.0, 

+      0.2, 

+  0.47 

a    Arietis      .     .     . 

+      0.9, 

+     1-5, 

+      1.4, 

+  1.22 

X    Draconis   .     .     . 

-     0.7, 

-2.0, 

-     1-4, 

-   1.74 

—  1.48 

f  Ceti       .... 

+     0.5, 

+      1-1, 

+  0.92 

A    Draconis,  S.  P.     . 

+      1.0, 

+     2.24 

+  1.80 

t    Cassiopeae      .     . 

—     0.9, 

-     1.0, 

+     0.  6, 

-  1.3, 

—  0.79 

v    Leonis  .... 

+      1.8, 

-     1.2, 

+      0.5, 

+  0.74 

i    Cassiopeos,  S.  P.  . 

+     0.2, 

+  0.20 

0    Leonis  .... 

+      1.5S 

+      0.5, 

+      1.7, 

+  i.o, 

+  1.45 

y   Ceti      .... 

-     0.8, 

+     1.1, 

-     0.8, 

—  0.63 

y    Ursse  Majoris     . 

0.0, 

+      0.1, 

+      0.2c 

+    1.1, 

+  0.38 

«   Ceti       .... 

—     0.64 

+     1.3, 

_     0.1, 

—  0.04 

o    Virginia     .     .     . 

-     0.24 

+      0.  16 

—  0.03 

48  (H)Cephei     .     . 

-     0.8, 

-     1.4, 

-     1.0, 

—  1.07 

4    (H.)  Draco.     .     . 

-     1.6, 

-     3.5, 

-     1.5, 

-   1.7. 

—  1.87 

48  (H)  Cephei,  S.P.  . 

+      1.6, 

+      0.  94 

+  1.20 

4    (H.)  Draco.,  S.P.  . 

+     2.2, 

+      1.9, 

+  2.05 

S    Arietis      .     .     . 

+      0.7, 

+      1.5, 

+  1.27 

i)    Virginis    .     .     . 

+      L74 

+     0.4, 

+      1.0, 

+  1.12 

o   Persei  .... 

0.0, 

-     0.4, 

+      0.1, 

-  0.9, 

—  0.26 

0   Corvi    .... 

-     0.  14 

—     0.9, 

—  0.61 

1    Tanri    .... 

+     0.3. 

+      1.3, 

+     0.5, 

+  0.57 

K    Draco  

-     1.9, 

-     1.1, 

-     1.2, 

_  1.2, 

—  1.27 

g   Persei  .... 

+      1.6, 

+     2.6, 

+  1.93 

«t    Draco.,  S.  P.    .     . 

+      1.7, 

+  1.70 

y    Eridaui      .     . 

+     0.74 

+     0.7, 

+  0.70 

32  (H.)  Camelop.     . 

—     3.3, 

—     2.4, 

-     1.2, 

-  iO, 

—  2.02 

Y    Tanri    .... 

+    i.o, 

—     0.6, 

+      0.8, 

+  0.72 

a    Canum  Venat.     . 

+     0.  5, 

+      0.9. 

+  0.75 

t    Tauri    .... 

+     0.1, 

-     0.2, 

+     0.5, 

+  0.35 

e    Virginis     .     .     . 

+     0.64 

+      1.1. 

+    2-0, 

+  1.16 

a    Tauri    .... 

+      1.7. 

+     2.2, 

+      1.6, 

+   2.4, 

+  1.80 

a    Virginis     .     .     . 

+      0.7, 

+     0.  4, 

+      0.9, 

+  i.o4 

+  0.81 

a    Camelop.   .     . 

+     0.5, 

+      0.2, 

+     0.8, 

-  0.3, 

+  0.30 

£    Virginis    .     .     . 

+      1.1. 

—     0.2, 

+      LI. 

+   0.64 

+  0.85 

o    Camelop.,  S.  P.    . 

-     1.0, 

—  1.00 

D    TTrsse  Majoris     . 

0.0, 

0.0, 

+     0.5, 

+  0.2, 

+  0.28 

i    Aurigae      .     .     . 

+      0.  7, 

+      1.0, 

+  0.90 

i)    Bootis  .... 

+      0.68 

-     0.2, 

+     0.7, 

+  0.24 

+  0.47 

11  Orionis      .     .     . 

+     0.8, 

. 

+      1.7, 

+    1.4, 

+  1.29 

a    Draconis    .     .     . 

-     0.7, 

-1.6, 

_     1.64 

_  1.44 

—  1.38 

o    Auriga}      .     .     . 

+     0.2, 

+      1.1, 

+  0.80 

a    Bootis  .... 

+      1.5. 

+      1.3, 

+     2.1, 

+   2.3, 

+  1.87 

0   Orionis      .     .     . 

0.  0, 

+      0.8, 

+      0.7, 

+    0.5, 

+  0.45 

fl    Bootis  .... 

+     0.4, 

-     0.6, 

-     0.2. 

0.04 

—  0.14 

0   Tauri    .... 

—     0.3, 

-     0.2, 

+     0.3, 

+    1.9, 

+  0.25 

5    UrsflB  Min.      .     . 

-     0.6, 

-     1.3, 

-     1.74 

_   1.3, 

—  1.32 

6    Orionis      .     .     . 

+      0.24 

-     0.2, 

—  0.02 

5    TJrBseMin.,S.P.  . 

+      23, 

+  2.30 

t    Orionis      .     .     . 

0.05 

+      0.  86 

+  0.44 

t    Bootis  .... 

+      0.16 

-     0.1, 

+      0.4, 

+   0.6, 

+  0.28 

a    Columbae  .     .     . 

+     3.4, 

+  3.40 

a'  Libne   .... 

+      1.6, 

+      1.4. 

+   1.6, 

+  1.51 

a    Oriouis      .     .     . 

+      0.36 

+     0.4, 

+      0.8, 

+    1.7, 

+  0.74 

0    UrsSD  Min.      .     . 

-     2.0, 

-     1.1, 

-     1.1« 

_  1.5, 

—  1.34 

li    Geminornm   .     . 

—     0.5, 

+      0.2, 

—  0.20 

0   TTrsas  Min.,S.  P.  . 

+      0.3, 

+      0.5, 

+  0.42 

y    Geminorum    . 

+      0.  3S 

+      0.9, 

+  0.62 

0   Librae  .... 

+     0.4, 

+     0.2, 

+      2.0, 

-  0.2, 

+  1.00 

51  (H)  Cephei     .     . 

+      0.  35 

+     0.  6, 

+  0.48 

[i    Bootis  .... 

+     0.2, 

0.  05 

+  0.08 

51  (H)  Cephei,  S.P.  . 

-     0.6, 

+      0.2, 

—  0.24 

y2  Ursse  Minoris 

-     1.3, 

-     0.1, 

+     0.5, 

—  0.30 

a    Canis  Majoris 

+      1.8, 

+      2.4, 

+  2.12 

a    CorouaeBorealis  . 

+      2.1. 

+      1.8, 

+      3.0, 

+    1.64 

+  2.30 

i     Canis  Majoris     . 

—     0.  55 

-     0.76 

—  0.60 

a    Serpentis  .     .     . 

+      1.86 

+      L33 

+      1.9. 

+    1.9S 

+   1.79 

6    Canis  Majoris 

+      0.63 

+  0.60 

t     Serpentis  . 

+    i.o. 

—     0.8, 

+      0.8, 

+   0.2, 

+  0.63 

S    Geminorum    . 

+     0.44 

0.0, 

+     0.  9, 

+  0.66 

£    TJrsSD  Minoris 

-    i.o, 

-     0.54 

i       0.  1, 

+    1-2, 

—  0.  22 

a2  Geminorum    . 

+      1.3. 

+      0.  76 

+  0.96 

i    Scorpii.     .     .     . 

+      1.8, 

+      1.  05 

+  1.23 

a    Canis  Minoris 

+     0.  76 

•;-      1.1, 

+    1.83 

+  1.08 

0    Scorpii 

1       L64 

-     0.1, 

+  0.66 

0    Geminorum    . 

1-     0.  75 

!-     0.  7, 

+  0.70 

i    Opliitichi  .     .     . 

i       1.04 

+     0.  5, 

+      0.8, 

+    0.4, 

+  0.72 

<tt    Geminornm    . 

-     0.1, 

{       0.  53 

+  0.26 

r    Herculis    .     .     . 

0.04 

0.0, 

-     O.ls 

—  0.3, 

—  0.09 

15  Argus  .... 

-1-      1.1, 

+     0.  86 

+  0.88 

a    Scorpii  .... 

+      1.9, 

h      1.6S 

+  1.74 

c    Hydree  

4-      13. 

+      1.  07 

+    3.  1, 

i    1  07 

fl    Draconis 

t-      0.  43 

+  0.40 

i    TTrste  Majoris 

T         i  .  •  '•; 

-     0.7, 

-     1-7, 

—     0.6, 

0.0, 

T-  x.  ^i 
—  0.75 

A  Draconis    .     .     . 

—     0.5, 

+      0.  4, 

+     0.8, 

+   0.9, 

+  0.40 

<r2  Ursae  Majoris 

-     2.0, 

-     1.6, 

-     2.23 

-   2-4, 

—  2.18 

I    Ophiuchl  .     .     . 

+     1.1. 

+      1.2, 

-      1.33 

+   0.94 

+  1.13 

o3  TTrsae  Maj.,  S.  P.  . 

+     1.8, 

T     2.24 

+  2.07 

?)    Herculis    .     .     . 

+    i.o4 

+      0.6S 

+  0.77 

POSITIONS    OF    FUNDAMENTAL    STARS.  39 

CORRECTIONS  TO  THK  XOUT11   1'OI.AK  DISTA  XfKS  (II    TMK  ST  MIS  OK  T1IK   AMKHH'AX    KIM1KMKHIS.  4T.-<:..nti,nl«l. 


Star. 

I860. 

1867. 

Mean. 

Star. 

1666. 

1867. 

Meau. 

D. 

R. 

D. 

R. 

D. 

R. 

D. 

R. 

„ 

„ 

„ 

„ 

// 

„ 

II 

a 

„ 

„ 

r    Ophiuchi  . 

t      1.  14 

-     1.1, 

0.0, 

+  0.20 

t    Delphiui    .     .     . 

+     0.6, 

+      0.8, 

0.0. 

+  0.38 

t     r  ,  «.!•  Minoria     . 

-     0.  34 

-     0.5, 

+      0.2, 

-  0.7, 

—  0.25 

a     Cyglii   .... 

+     0.5. 

+     1.3, 

I      0.6, 

+    2.1, 

+  0.74 

«    Hrculin      .     .     . 

+     1-8, 

+      0.9, 

+     1.8, 

+   !•», 

+  1.60 

/i    Aquarii     .     .     . 

+     0.6, 

+     1.1, 

+      1.4, 

+    1.5, 

+  1.18 

6    Optiiiu'hi  .     .     . 

4-      1.  0, 

+     0.8, 

+  0.89 

r    Cygni   .... 

+     1.4, 

+     0.5, 

+  0.86 

a    Ophiurhi  .     . 

+     2-5. 

+     1.8, 

+     1.8. 

+    1.2, 

-i    1.92 

61  Cygni   .... 

0.0, 

-    0.2, 

—  0.12 

cj   Draconis   . 

-     1.6, 

-1.8, 

-     2.2, 

-   1.9, 

—  1.91 

I    Cygni  .... 

+      0.4. 

+     0.2, 

+     0.8, 

+    0.5, 

+  0.32 

a    lii.irom*.  S.  P.     . 

i       2.4, 

+  2.40 

*    Cephei  .... 

-     0.94 

-     1.34 

-     1.2. 

+    0.1, 

—  0.91 

f     Hercnlii    .     .     . 

+     0.9, 

+     1.2, 

0.0, 

+  0.18 

a    Cephei,  S.  P.  .     . 

+      1.6, 

+  1.60 

i/<    ]>rai  "ni.s 

1       0.  4, 

+  0.40 

1    Pegasi  .... 

r      1-7, 

+     3.3, 

1      2.  5, 

+  2.50 

y    Dracouis   .     .     . 

j      0.3, 

+     1.0, 

+      0.2, 

+    0.  14 

+  0.36 

0   Aqnarii     .     .     . 

+      0.84 

0.0, 

+     0.  4, 

+    1-5, 

+  0.66 

r'  Sagittarii  .     .     . 

-     0.4, 

—  0.40 

0   Cephei.     .     .     . 

-     1.2, 

-0.6, 

-    0.8, 

—   1.0, 

—  0.91 

f    Suttittarii  .     .     . 

+     O.G, 

-     0.6, 

0.00 

0   Cephei,  S.  P.  .     . 

+      1.2, 

+  1.20 

1    Serpentis  .     .     . 

+    i.o, 

0.0, 

+  0.40 

£    Aquarii     .     .     . 

+     1-0, 

+     0.4, 

+  0.64 

1    Ureas  Minoria     . 

-1.26, 

-     0.37, 

-1.40, 

—  0.68, 

—  1.09 

{  Pegasi.     .     .     . 

+      0.54 

+    i.o, 

+     0.5, 

+  0.9, 

+  0.49 

1    UrewMin.,S.  P.  . 

+     0.57, 

.     . 

+     0.99, 

+  0.81 

11  Cephei.     .     .     . 

-     LI, 

-     1.04 

-    0.5, 

—  6.86 

1    Aqnilo;      .     .     . 

-     0.74 

+     0.9, 

-     0.5, 

-  1.9, 

—  0.45 

i\    Capricorni 

+     0.0, 

+      0.4, 

+  0.57 

a    Lyrae    .... 

+      0.6, 

+      1.3, 

+  0.99 

79  Draconis   .     .     . 

—    0.5, 

-  1.0, 

—  0.75 

ff    Lyra)    .... 

-     0.34 

-     0.3, 

—  0.30 

79  Draconis,  S.  P.     . 

+     1.6, 

+  1.60 

*    Sacittarii  .     .     . 

+      1.0, 

+      1.2. 

+   1.12 

a    Aqnarii     .     .     . 

+     1.  4, 

+     0.9, 

+     0.6, 

+    1.2, 

+  1.00 

50  DraconU   .     .     . 

-     1-1, 

-     12, 

-     1.2, 

-  l.I» 

—  1.15 

9     Aquarii     .     .     . 

+      1.44 

+      1.2, 

+     0.8, 

+  0.9, 

+  1.M 

g    AquilaB      .     .     . 

+     0.94 

+     2.2, 

+    1.0. 

+   1.4, 

+  1.15 

JT    Aquarii     .     .     . 

-     0.4, 

+     2.4, 

+      0.6, 

+  0.48 

i    Uraconia    .     .     . 

—     0.8, 

-     1.1, 

-     0.74 

-  0.2, 

—  0.55 

1    Aquarii     .     .     . 

+     0.94 

+     0.4, 

+      0.9, 

+  0.85 

T    Draconis  .     .     . 

—     0.6» 

-  0.3, 

—  0.42 

g    Pegasi.     .     .     . 

+     1.5. 

+     0.8, 

+      1.5, 

+  1.37 

5    Aqnilffl       .      .     . 

4-     0.  G, 

+     1.6, 

1      0.  9, 

+    1.3, 

+  0.97 

i    Cephei  .... 

-     0.4, 

+     0.1, 

-     0.6, 

-  1.0, 

—  0.46 

1C      Aquil.r         .       .       . 

+     0.6, 

+     0.4, 

+     0.8, 

+    0.6, 

+  0.69 

i    Cephei,  S.  P.  .     . 

+      1.3, 

+  1.30 

Y    AquiliB       .     .      . 

+      1.54 

+     3.1, 

+     1.5, 

+   1.63 

A    Aquarii 

+     0.9, 

+     1.8, 

+     0.14 

+    1.1, 

+  0.69 

a    Aquihe 

f      1.0, 

+     1.4, 

+  i.o, 

+  1.19 

a    Piscis  Australia  . 

+     1.3, 

r     0.6, 

+  0.81 

i     Draconis   .     .     . 

-     1-1, 

-   1.9, 

—  1.50 

a    Pegaai  .... 

+     1.84 

+     2.8, 

+     2.9, 

+   2.1, 

+  3.15 

0    Aquilie      .     .     . 

+     0.  7, 

+     1.0, 

+  0.90 

o    Cephei  .... 

-     1.6. 

-  0.8, 

—  1.30 

A    Une  Minoris     . 

+     0.9, 

+     0.2, 

-  0.9, 

+  0.  IS 

o    Cephei,  S.  P.  .     . 

+     1.6, 

+  1.60 

A    UnuB  Min.,  S.P.  . 

0.0, 

-     0.1, 

—  0.05 

8    Piscium     .     .     . 

+      0.  7, 

+     0.2, 

+     0.8, 

0.0, 

+  0.28 

T       Aiplil."         .        .        . 

+     0.8, 

+     1.3, 

+  1.00 

t    Piscium     .     .     . 

+     0.5, 

+      0.4, 

+  0.5, 

+  0.45 

a1  Capricorni 

+      1.  0, 

-     0.4, 

+      1.  1. 

+    1.1, 

+  0.85 

y   Cephei  .... 

-     0.94 

-     0.1, 

-     0.3, 

—  0.5, 

—  0.53 

K    Cephei  .... 

-     1.0, 

—  0.9, 

—  0.95 

f   Cephei,  &  P.  .     . 

—     2.7, 

+     0.  1, 

—  0.37 

<r    Cephei,  S.  P.  .     . 

+     0.8, 

+  0.  80 

w  Piacium     .     .     . 

0.0, 

+    i.o,- 

+    o.», 

+  0.64 

ir    Capricurni      .     . 

+      1.94 

+     1.4, 

+  1.62 

MEAN  POSITIONS  OF  THE  STANDARD  STARS  FOR  THE  FICTITIOUS  EPOCH,  1870.0. 

The  preceding  investigation  has  resulted  in  furnishing  us  for  each  co-ordinate  and  each  star  a 
certain  mean  correction  applicable  to  the  ephemeris  of  the  star  at  the  epoch  corresponding  to  the 
mean  of  the  times  of  observation.  The  ephemeris  in  question  is  that  given  in  the  American 
Ephemeris  for  the  years  1865-'69.  The  mean  epoch  is  different  for  every  star,  but  may,  without 
appreciable  error  in  any  case,  be  supposed  18G7.0  for  all  the  polar  distances,  and  for  the  right  ascen- 
sions of  the  circumpolar  stars,  which  are  not  found  in  the  column  "  result  of  transit,"  and  1865.0 
for  the  right  ascensions  of  all  other  stars.  If  Ae  represent  the  error  of  the  epoch  thus  assumed, 
and  J  IJL  the  error  of  the  adopted  proper  motion,  the  error,  from  application  to  the  wrong  epoch,  will 
be  only  Je  x  J,«,  a  quantity  which  will  probably  be  insensible  in  all  cases. 

The  epoch  being  variable,  the  decennial  epoch  1870.0  has  been  selected  for  the  preparation  of 
the  catalogue.  In  deducing  the  right  ascensions  for  1870.0,  the  positions  are  carried  forward  from 
the  mean  epoch  to  1870,  with  the  annual  variations  of  the  ephemeris  of  comparison.  That  is,  the 
deduced  correction  is  applied,  not  to  the  mean  place  of  the  ephemeris  at  the  mean  epoch,  but  to  that 
for  1870.0. 

The  catalogue  thus  obtained  is  as  follows. 

The  column  "  Weight."  of  the  north  polar  distances  gives  the  number  of  independent  standard 
observations  to  which  the  observations  actually  made  are  considered  equivalent. 


40  POSITIONS    OF    FUNDAMENTAL    STARS. 

The  precessions  here  given  have  been  independently  computed  from  Struve's  value  of  the  con- 
stant, using  the  tables  in  the  Washington  Observations  for  1847. 

The  secular  variation  of  the  precession  means,  as  usual,  one  hundred  times  the  second  deriva- 
tive of  the  co-ordinate  for  the  epoch  of  the  catalogue.  But,  instead  of  being  independently  com- 
puted, it  is  deduced  from  the  values  given  in  Table  XXI  of  the  "  Star  Tables  of  the  American. 
Ephemeris  "  for  I860.*  The  value  for  1870  was  supposed  the  same  as  for  1860,  except  in  the  cases 
of  those  circurnpolar  stars  for  which  Dr.  Gould's  standard  catalogue  gives  the  mean  right  ascen- 
sion developed  in  powers  of  the  tiine.t  Here  Dr.  Gould  gives 


-f-etc., 
t  being  reckoned  from  1855.0.    Differentiating  we  have 


Whence,  for  the  change  ia  -ja,  between  1860  and  1870,  we  have,  by  putting  t  =  5,  and  t=  15,  and 
taking  the  difference, 

ffta 

A  1^  =  600  +  2400  D  +  etc. 

(it 

The  value  of  100  J  -r^thus  obtained  was  applied  to  the  secular  variation  given  in  the  star  tables  to 

Wf 

reduce  it  to  1870. 

The  proper  motions  here  given  are  those  of  the  catalogue  of  comparison,  and  therefore  are 
effectively,  those  actually  employed  in  bringing  forward  the  positions  from  the  mean  epoch  to  1870.  If 
we  require  the  positions  for  the  mean  epoch,  as  deduced  from  the  observations,  without  any  hypothesis 
respecting  the  proper  motion,  we  have  only  to  reduce  each  co-ordinate  back  to  the  epoch  with  this 
given  proper  motion.  And  if  we  take  for  the  mean  epochs  those  already  indicated,  namely,  1867.0, 
for  all  the  polar  distances,  and  for  the  right  ascensions  of  the  few  stars  not  determined  with  the 
transit  instrument,  and  1865.0  for  all  other  right  ascensions,  the  epoch  will  seldom  or  never  be  a 
year  in  error,  and  the  error  introduced  will  seldom  or  never  exceed  the  error  of  the  adopted  annual 
proper  motion,  which  will  be  entirely  unimportant. 

The  last  column  corresponding  to  each  co-ordinate  gives  the  difference  between  the  value  of 
the  co-ordinate,  as  printed  in  this  catalogue,  and  that  given  in  the  American  Ephemeris  for  1870. 

*  Tables  to  facilitate  the  reduction  of  places  of  the  fixed  stars,  prepared  for  the  use  of  the  American  Ephemerie  and 
Nautical  Almanac.  Washington,  1869. 

t  Standard  mean  places  of  circumpolar  and  time  stars,  prepared  for  the  use  of  the  Coast  Survey,  second  edition. 
Washington,  1866. 


POSITIONS    OF   FUNDAMENTAL   STARS. 


41 


MKAN  I'osinoNs  FIH;  wmfl  1.1  \NTAKY  o,/. -0,7.11;.  WASIIINC  niv>  UK  STAKS  OF  THE  AMERICAN  F.I'IIFMF.KIS,  DEDUCED 

FROM   (HiSFKVATIONS   WITH     I  III:   TRANSIT   IXSTRTMKXT   ANI>  THE  TRANSIT  CIRCLE   DURING  THE  YEARS  1862-'67. 


SI.  II. 

ij 

7~ 
i_ 

o 

-i 
(4 

i 

i 

11 

| 

CHIT'II  to  Am. 
EphciiL.  1874 

J 

1 

0 

a 
ri 
ri 

j 

Secular  varia- 
tion. 

i 
ii 

41 

ii 

k.  m.  t. 

>. 

t. 

1. 

t. 

O        I        It 

// 

// 

// 

„ 

•        Xlnll.'lit.  .]..       . 

119 

0     1  40.344 

-i    3.0773 

+     .  0182 

+  .0102 

+     .050 

16 

61   37  39.  10 

—    20.054 

+  0.011 

t-  0.146 

+     1.96 

)      IVlMM             .       . 

n 

0    6  32.  «5:i 

a.  OBU 

•      .0100 

j-  .0006 

<      .035 

15 

75  32  22.  14 

—    20.  047 

+  0.020 

(-  0.011 

+     1.46 

a     C:is.Hi,iiN'jt!  . 

18 

0  33    C.B7 

I    3.3559 

+     .0550 

+  .0076 

—    .01 

11 

31   III  :tt.  ."7 

—    19.845 

+  0.088 

r  0.  034 

—    0.08 

li  (Yti  .... 

90 

0  37    :l  rt>3 

i     2.  W3 

—    .  i»i:>7 

.11113 

+     .083 

13 

III-  12    2.65 

—    19.  793 

+  0.079 

—  0.020 

-)-     0.  93 

•-'1     *  'llSHiop.-H!   . 

u 

0  37    6.  46 

3.  SI7I 

f     .  1581 

—  .0114 

4-     .08 

10 

15  43  23.07 

—    19.792 

+  0.0% 

|    0.060 

—    1.89 

f        I'i-t  iUlll          .        . 

135 

0  56  11.931 

+  3.1130 

+     .0086 

—  .0035 

4-     .052 

13 

8*  48  38.  53 

—    19.455 

I-  0.  117 

0.000 

4-     1.81 

Polaris  .     .     . 

7 

1    11   17.  34 

+20.014 

+  14.240 

+  .073 

—    .33 

56 

1  23    1.47 

—    19.  092 

+  0.910 

—  0.006 

—    0.07 

H     C,.|i          .       .       . 

n 

1  17  31.  .V.'l 

;   3.0113(1 

+     .0(117 

—  .  IXI.-,3 

:        .  UM 

10 

98  51  18.  47 

—    18.918 

+  0.152 

I    0.220 

+     1  90 

il     risciinn      .     . 

in 

1  24  ::i  OH 

:i.  I'.i-i 

+     .0142 

•     .  IHHI'.I 

1       .IH.C.I 

14 

75  19  31.71 

—    18.  706 

+  0.  175 

0.000 

+     1.91 

"      l'i*rium 

63 

1  3*  :u.!ii4 

3.  i.v.i 

j      .11111 

+  .0061 

+     .003 

13 

81  29  52.  17 

—    18.230 

+  0.199 

—  0.009 

I-     1.  24 

,1     \ii.ti-.  .      .      . 

117 

1  47  27.  779 

+  3.2841 

+     .  0182 

+  .OOC2 

+     .045 

14 

69  49  43.  85 

—    17.891 

+  0.224 

(-  0.109 

+     1.81 

."•41   (  '.i-sii.|if;i-  . 

111 

i  :••_•  2:1.111 

1.  '.i.-iil 

I-:. 

—  .011 

+     .04 

7 

18  12  35.  21 

—     17.  692 

0.345 

0.000 

—    0.43 

a     Aril-tin  .      .      . 

M 

i  59  5o.  IKK  > 

:i.  3534 

4-     .0203 

i     .II14-J 

+     .038 

16 

67    9  13.53 

—    17.375 

H-  0.253 

+  O.i:t7 

4-     1.35 

i'  c,-ii  .... 

4* 

2    6    6.  736 

i   3.  1733 

+     .0115 

—  .  OtH'J 

+     .072 

10 

81  45  52.50 

—     17.  095 

I    0.248 

I-  0.040 

+     0.86 

t     C:iHMiulM-lB  . 

8 

2  18  23.  41 

i.  -u 

+     .1300 

—  .008 

+     .86 

7 

23  11     a  46 

—     16.508 

H-  0.404 

+  0.020 

—    0.74 

)•     Ci-ti  . 

44 

2  36  34.  016 

:     3.  Illl. 

+     .0092 

—  .0094 

4-     .031 

11 

87  18  49.  43 

—     15.556 

+  0.291 

|-  0.  191 

-r     1.  18 

a     (Vti  .... 

71 

2  55  29.  188 

r  3.  1300 

i-     .0097 

—  .0015 

+     .050 

13 

86  25  19.  29 

—    14.  459 

+  0.321 

|-  0.  103 

i      0.  42 

!:•    C.  pll.'i     .       .       . 

M 

3    3  55.  35 

+  7.322 

+     .350 

+  .016 

+     .12 

11 

12  44  50.  92 

—     13.  9X> 

+  0.770 

+  0.066 

—    0.13 

a     Arii-tis  .     .     . 

24 

3    7  25.  951 

3.  1:11-  1 

+     .  0176 

—  .0015 

—    .008 

7 

69  26  21.  86 

—     13.714 

+  0.370 

+  0.071 

+     1.80 

a     IVrm-i    .     .     . 

24 

3  15    a  19 

i     4.  245  I 

+     .0483 

+  .0020 

4-     .06 

10 

40  36  14.  58 

—    13.220 

+  0.470 

+  0.043 

—    0.  30 

>I    Tauri     .     .     . 

68 

3  39  45.629 

i    3.5525 

+     .0173 

+  .0010 

+     .035 

13 

66  17  57.30 

—    11.520 

+  0.430 

4-  0.060 

4-0.93 

<       Pl-Wi       .        .        . 

8 

3  45  57.  894 

i-  3.7551 

+     .0222 

+  .0006 

+     .022 

3 

58  30  19.  58 

—    11.072 

+  0.460 

+  0.049 

+     2.25 

j-     Kriihuii 

38 

3  51  57.948 

2.  7!  120 

+     .  0045 

+  .0044 

+     .067 

7 

103  52  49.  62 

—    10.  630 

+  0.350 

+  0.  120 

i      2.  30 

y    Tauri     .     .     . 

41 

12  23.  .-71 

;  a  3983 

+     .0116 

+  .0085 

+     .038 

10 

74  41  19.90 

—      9.  074 

+  0.447 

+  0.031 

+     1.71 

c     Tauri     .     .     . 

55 

21     1.  674 

+  3.4876 

+     .0122 

+  .0076 

+     .  019 

10 

71     6  37.  91 

—      8.395 

4-  0.467 

+  0.031 

+     1.73 

«    Tauri     .     .     . 

151 

28  37.806 

+  a  4311 

+     .0106 

+  .0045 

t.  (Ill 

18 

73  45  16.  86 

—      7.793 

+  0.465 

+  0.166 

+     1.71 

a    Cami-liipiinli    . 

13 

41    .-.  i:-j 

+  5.915 

+     .070 

—  .003 

.17 

10 

23  52  56.  91 

—      6.765 

+  0.814 

—  0.009 

f     0.  44 

t        \illit:;r 

37 

48  31.  808 

+  3.8971 

i-     .0146 

—  .0008 

—    .011 

9 

57    2  34.  21 

—      6.153 

+  0.543 

+  0.020 

+     1.  6C 

11  Ormnis  .     .     . 

28 

57    a  536 

|    3.  4-.MI 

4-     .0078 

(-  .0025 

—    .037 

8 

74  46  46.  94 

—      5.  432 

+  0.483 

+  0.031 

+     1.67 

a    Aurlgie      .     . 

17 

5    7    5.30 

f  4.4134 

4-     .0160 

+  .0086 

—    .03 

3 

44    8  15.38 

—      4.  5r» 

-j-  0.630 

+  0.420 

+     0.40 

0   Orion  is  . 

120 

5    8  17.  481 

+  2.8808 

+     .  0040 

—  .0001 

+     .025 

18 

98  21  15.  03 

—      4.486 

+  0.411 

+  0.017 

4-     1.13 

11    Tiiuri     .     .     . 

111 

5  18    4.  523 

+  3.  7h.V 

.  M 

t    .0017 

+     .010 

17 

61  30  19.  51 

—      3.648 

+  0.545 

I    0.191 

4-0.96 

<'     Idiiinm  .      .     . 

78 

5  2521.970 

3.  (MW.I 

4-     .  0038 

t-  .0009 

—    .004 

9 

!K>  23  52.65 

—      3.  019 

+  0.443 

+  0.040 

4.     1.01 

a     I  .  |>"ii-       .     . 

15 

5  26  59.879 

i-  2.IM44 

.      .  IXKIII 

.  (Klil 

—    .010 

107  55 

—      2.878 

+  0.383 

0.000 

'     Onoiiis  . 

79 

5  29  37.  077 

+  3.  (Mi! 

+     .0036 

—  .0005 

4-    .023 

11 

91  17  14.93 

—      2.651 

c  0.441 

+  0.011 

+     1.23 

.1    ('"luniliiB    .     . 

19 

5  34  56.  569 

+  2.  1709 

+     .0028 

4-  .0026 

—    .011 

I 

124    8  43.  52 

—      2.178 

4-  0.316 

0.000 

+     2.53 

a    <  iiinuis  . 

144 

5  48    H.  II7-J 

+-  3.-J15I 

+      .  IKI-JS 

+  .11017 

4-    .003 

18 

82  37  11.89 

—      1.038 

4-  0.  474 

0.000 

+    l.U 

li    1  M-niiiiornni     . 

38 

6  15    5.755 

-f-  3.  i;-;n:i 

—    .  0004 

+  .0059 

—    .007 

7 

67  25  21.  32 

+       1.320 

+  0.529 

4-  0.  140 

4-     1.32 

)     lii'tiiinot  inn     . 

13C 

6  30  12.  1  l.'i 

i-   3.  Hi  111 

—    .0014 

4-  .0040 

—    .(in 

13 

73  --"I  33.  00 

4-      2.635 

+  0.  501 

4-  0.040 

4-     1.44 

.M  c.-pli.-i   .     .     . 

47 

6  38  43.  17 

+30.406 

—  2.011 

-  .106 

4-    .17 

21 

2  45  37.  67 

-j-      3.373 

+  4.341 

—  0.  003" 

—    O.S8 

«   CantaMajoris  . 

134 

6  39  25.  074 

f  2.  GWIB 

.0000 

—  .  0364 

[-  .054] 

13 

106  32  25.02 

4-       3.  371 

4-  0.381 

f  1.383 

4-    2.64 

r      I  'llllis  M;ij..l  i> 

44 

6  53  31.066 

•j.  x,;  i 

1-     .  0013 

+  .0013 

—    .019 

10 

118  47  49.74 

+       4.638 

|-  0.333 

+  0.020 

+     1.  32 

t    Citnis  Miijori.H  . 

11 

7    :i    ii.  3> 

•j.  i.i'.i.. 

f     .0012 

+  .0003 

—    .1111; 

3 

116  11  18.79 

+       5.453 

+  0.340 

—  0.009 

+     1.67 

''     <  ii-miii"!  urn 

53 

7  12  21   455 

:i.  .v.nii 

—     .  IXIVJ 

-  .0004 

—    .026 

13 

117  4(1  52.  in 

+       6.227 

+  0.496 

+  0.020 

i        1.H1 

0*   (iclllill.n  Mill 

76 

7  26  18.  121 

3.  -.Ml 

—     .11131 

—  .IIH'.I 

i      .  ->7(l 

10 

57  49  45.  77 

+       7.  374 

+  0.527 

+  0.076 

4-0.97 

a    Cani>  Minmis 

167 

7  33  29.  718 

3.  1III7 

—    .0042 

—  .057 

—    .110 

16 

84  26  39.  52 

+       7.876 

+  0.420 

[+1.040] 

+     1.09 

&    Gfininorum     . 

149 

7  37  21.  -500 

3.  7-J.HI 

.ill-.'.'. 

—  .11171 

—    .0114 

14 

111   :I9  44.81 

+       R262 

+  0.480 

|    0.060 

t      1.41 

t    '  i.'iiiiimriini     . 

IS 

1  45  :w.  M:, 

—     .11130 

_  1 

—    .050 

5 

ii-'  M     1.95 

+       8.  913 

+  0.478 

+  0.049 

+     1.71 

l."i  Ar^iin    .     .     . 

23 

ii  :,!•; 

•„'.  Mf.t 

(Mill 

—  .0046 

—     .  032 

8 

113  55  53.08 

I      10.  179 

4-  0.317 

—  0.060 

+     1.83 

«    Hydno  .     .     . 

60 

8  39  53.  451 

:i.  I'.KKI 

—    .0071 

—  .11117 

—    .012 

10 

83    6  22.65 

+     12.884 

I    0.350 

+  0.040 

+     1.98 

i    Urai'  Mrtji'ii-1 

!     4  1C70 

—    .0444 

—  .  0453 

4 

41  26  59.65 

+     13.  568 

+  0.  436 

+  0.280 

—    0.80 

ff1  Ursa?  Majoria  . 

13 

8  'S8'  55.'  15 

-  1     —    .  134 

—  .  IKK 

—  .'of 

11 

24  20  25.  3« 

!     .14.114 

u  tee 

h  0.097 

—    2.  15 

It     1  ':nn-i  i     .      .      . 

•J4        11    II  42.  254 

3,  -ivs  _    .  INI:I  i 

—  .OIKIO 

+     .020 

7 

7."   IH  37.92 

14.  CM 

0.  3-.-.I 

+  0.011 

+     1.77 

1    DracunU    .     . 

6       9  If  31.  l:t 

U.  l(i<l     —    .  W07 

_   .  IKI- 

—    .17 

9 

8    0  10.37 

1-     15.  269 

+  0.873 

—  0.006 

(-     0.68 

a    Hyilrjc  .     .     . 

89       9  21  11.956 

•J.  1I.VI7 

—    .0014 

—  .0011 

+     .001 

16 

98    5  47.  96 

+     15  430 

:    0.  'JCll 

—  0.040 

+     1.45 

8    TJnw-Mii.j.ni- 

4       9  24    8.  88 

1.  I..-7 

—    .0553 

—  .  nun 

f     .04 

2 

37  43  54.  98 

+     15.  594 

+  0.357 

+  0.569 

+     0.05 

r     I...  mis    .      .      . 

<•'-,       9  38  28.  l»7 

a.  oas         BITS 

—  .  002." 

—    .oil 

U 

115  37  43.56 

+     16.  351 

0.2.-3 

+  0.020 

i      1.54 

(i    Leonfo  .     .     . 

37        «  45  21.  nil 

3.  1  (35    —     .  01117 

—  .0188 

+     .020 

8 

63  22  56.  13 

111.  I1!I3 

+  0.270 

+  0.060 

{      1.01 

a     I.  ••..iiis  .     .     . 

119      10     1  26.820 

3.  -.'•.'IKI    —    .0101 

—  .0165 

—    .014 

19       77  23  55.  K 

4-     17.  431 

(I.  •.'•il 

—  fl.Oll 

1.  .VI 

j     Leoois  .     .     . 

86 

10  12  48.  138 

:i.  -JC5    —    .015'J 

i    .0203 

4-     .014 

13 

69  30    7.86 

+     17.901 

+  0.213 

+  0.151 

+     2.08 

9    Draronis    .     . 

7 

10  23  58.  40 

+  5.317 

—    .284 

.000 

—    .08 

8 

13  37    6.  92 

+     ia320 

+  0.312 

I    0.031 

—     1.2H 

fLconin  .     .     . 

4v!      Ill  25  57.889 

:i.  lii.-,d 

—    .0081 

f  .0005 

—    .036 

8       80    1  31.  85 

+     1R390 

+  0.177 

.    11.034 

(      1.23 

1  U  .     .     . 

:.:,     in  42  25.  :»-,!> 

3.  iui:< 

—    .0082 

—  .0006 

+     .035 

12       78  46    4.06 

+     18.917 

.    0.146 

i    0.020 

|      1.S4 

a    I'ruH-Majorm.         41      10  55  41.  04 

_     Jl-,-.' 

—  .  0195 

.« 

14       -27  32  52.  18 

+     19.  270 

+  0.145 

+  0.086 

-    0.41 

HIM                .           • 

'M      11     7  11.525 

-r  3.  1908 

—    .0134 

+  .0117 

-     .027 

14 

68  45  5a05 

+     19.  525 

II.  1IKI 

+  0.  140 

!      1.  cl 

A    Crati-riH      .     . 

46      11  12  50.585 

3.IP037 

+     .0063 

—  .  C078 

f     .005 

9 

104    4  31.  88 

+     19.632 

n.  u-.' 

—  0.180 

+     1.35 

T       I.f.tllis    . 

2r-       11   21    I.'..  1-Jli           3.0-112 

—    .002J 

+  .0019 

+     .  012 

9 

86  25   II  M 

+     19.  769 

+  0.068 

>    0.020 

4-     1.11 

A     Draronin    .      . 

19     11  2.1  3:1.  :,:.          3.  i;:,:i 

—    .113 

—  .011 

+     .19 

16 

1957    6.11 

t      19.  803 

.    11.1177 

+  0.060 

—     1.53 

v    Leonifl  .     .     . 

56      11  30  17.  5!i9         3.1171- 

+     .0002 

.0000 

-    .008 

9 

90    6  23.  29 

+     1!>.  887 

+  0.050 

—  0.  031 

+     1.59 

II   Leonis  .     .     . 

116      11  42  25.660 

T  3.  1001 

—    .0073 

—  .0344 

+     .015 

17 

74  42    5.56 

+     19.  990 

+  0.026 

+  0.  103 

+     1.B7 

y   Urea-  Mnjoris  . 

18      11  46  58.98 

+  3.  178S 

—    .0440 

.-  .01  in 

+     .07 

12 

35  34  57.  42 

4-     20.023 

f  0.019 

—  0.  003 

+     0.51 

o    Virginia     .     . 

51      11  56  35.224 

3.  1173.', 

—    .00:12 

—  .0130  1+     .006 

10       80  32  42.  33 

+     20.055 

—  0.005 

—  0.020 

+     1.48 

4    Dnu-mim     .     . 

18      12    6    4.78 

-  2.900 

—     .  1-JH 

-    .010     '-       .06 

16       11  39  411  15 

+     20.  H48 

—  0.019    +  0.008 

_    1.90 

«    Virginin     .     . 
ft  Corvi     .     .     . 

69 
53 

12  13  15.348 
12  27  33.  735 

+-  a  0721 
r  ai3»s 

-     .  IKM;  —  .  (Ki:n   -    .  oofl 

+     .0163  U  .0041    —    .006 

13 
11 

89  56  40.  07 
112  40  39.  S3 

+     20.021 
+     19.  910 

—  0.  033 
—  0.  062 

+  0.029 
i    0.069 

+     1.86 
+     1.87 

42 


POSITIONS    OF    FUNDAMENTAL    STARS. 


MEAN  POSITIONS  FOR  1870.0  (JANUARY  Orf.— Od.16,  WASHINGTON)  OF  STARS  OF  THE  AMERICAN  EI'IIK  M  El:  IS,  \  r.— ( 'cuit  iniii-d. 


Star. 

1   . 
if 

7 

0 

i 

4 

M 

Precession. 

Secular  varia- 
tion. 

Proper  motion. 

Corr'll  to  Am. 
Epliem.,  1870. 

A 
i 

* 

o 

i 

o 

fi 

rf 

Precession. 

Secular  varia- 
tion. 

Proper  motion. 

CCIIT'II  to  Am. 
Eplicni..  1.-70. 

h.  m.  s. 

s. 

s. 

s. 

ftp 

0        /         // 

„ 

„ 

„ 

„ 

IT    Draconis     . 

5 

12  27  55.  31 

+  2.612 

—    .055 

—  .011 

+    .02 

8 

19  29  41.  59 

l-     19.  906 

—  0.054 

+  0.023 

—    1.32 

322Caiuelopanli    . 

9 

12  48  13.  51 

+  0.362 

+     .222 

—  .012 

+     .50 

11 

5  52  48.  81 

+     19.612 

—  0.018 

i-  0.030 

—    2.02 

a    (Jaiium  Ven.  . 

71 

12  4!)  56.  627 

+  2.  8379 

—    .  0151 

—  .  0204 

+     .027 

13 

50  58  4.1.11 

19.  SSI 

_  1).  036 

-  0.  Hill 

+     1.04 

0    Virginia     .     . 

83 

13    3  13.  268 

+  3.  1030 

+     .0077 

—  .  0024 

—    .OH 

12 

94  50  40.  76 

+     19.  297 

-  0.  130 

i-  0.040 

+     2.09 

a    Virginia      .     . 

200 

13  18  20.  852 

+  3.1551 

t-     .0114 

—  .  1:024 

+     .  015 

22 

100  28  55.  51 

f     18.  894 

-  0.  161 

i-  0.034 

:-      1.46 

£    Virginia      .     . 

94 

13  28    4.  261 

+   3.0715 

1-     .  C063 

—  .  0189 

+     .029 

17 

89  55  49.74 

+     18.  592 

—  0.  173 

—  I).  ODD 

+     1.59 

TI    UraD  Majoris  . 

24 

13  42  24.  99 

+  2.3844 

—    .01113 

—  .0102 

.00 

13 

40    2  13.  61 

18.0*7 

—  0.  156 

0.  020 

'••      II.  OH 

rt    Bootis    .     .     . 

inc. 

13  48  29.  713 

+  2.8617 

—    .0005 

—  .0031 

—    .016 

19 

70  56  59.35 

+     17.  851 

—  0.  197 

f    0.360 

i-      1.81 

a    Draconis    .     . 

13 

14    0  52.  30 

+  1.629 

+     .  0052 

—  .007 

+     .04 

12 

25    0    8.22 

+     17.  330 

—  0.  136 

\-  0.034 

-1.38 

a    Bootis    .     .     . 

186 

14    9  43.975 

+  2.8131 

+     .  0023 

—  .  0798 

+     .  033 

22 

70    8  23.  46 

+     16.  927 

—  0.214 

+  1.970 

t-     1.99 

6    Bootis    .     .     . 

18 

14  20  46.31 

+  2.0697 

—    .  0013 

—  .0266 

+     .08 

13 

37  32  51.  22 

+     16.  390 

—  0.  176 

i-  0.409 

D.W 

5    Ursa?  Miuoris  . 

13 

14  27  49.96 

—  0.  219 

+     .122 

+  .005 

+     .13 

11 

13  43  33.  95 

+     16.  025 

0.012 

+  0.  C20 

—     1.43 

c    Bootis    .     .     . 

88 

14  39  18.  612 

+  2.6241 

—    .  0001 

—  .0025 

+     .009 

15 

62  22  35.  79 

+     15.  402 

—  0.  250 

—  0.011 

;      1.35 

a2  Libra)    .     .     . 

81 

14  43  41.416 

+  3.3150 

+     .0155 

—  .0085 

+     .016 

14 

105  30    0.  22 

+     15.  153 

—  0.  321 

+  0.054 

+     1.  74 

0    UrsseMmoris  . 

57 

14  51     6.66 

—  0.  244 

+     .104- 

—  .007 

+     .02 

17 

15  18  47.  57 

+     14.  720 

+  0.020 

I-  0.029 

-    1.34 

fi    Bootis    .     .     . 

6 

14  57    2.  89 

+  2.2637 

.0000 

—  .0038 

—    .06 

49    5     .      . 

+     14.  362 

—  0.235 

+  0.060  |         .      . 

/?    Librae    .     .     . 

91 

15  10    0.866 

-|-  3.2265 

+     .0118 

—  .0067 

+     .031 

16 

98  54  6.  02 

+     M.  548 

—  0.  3.11 

i    0.009 

+     3.23 

ft    Bootis    .     .     . 

88 

15  19  34.  843 

f-  2.2780 

+     .  0012 

—  .0102 

+     .018 

8 

52    9  56.  26 

+     12.919 

—  0.  257 

—  0.  091 

r     0.61 

y    TJrstc  Minoris  . 

6 

15  20  57.  15 

—  0.  148 

+    .075 

.000 

—    .07 

6 

17  42  11.57 

+     12.827 

+  0.012 

—  0.  029 

—    0.30 

a    Corona?  Borealis 

140 

15  29  11.084 

+  2.5296 

+    .0024 

+  .0097 

+     .027 

21 

62  50  47.  50 

+     12.  265 

—  0.299 

+  0.063 

+     1.85 

a    Serpentis    . 

102 

15  37  51.  987 

r  3.9417 

+    .  0061 

+  .0085 

+     .051 

21 

83    9  49.  83 

+     11.  656 

—  II.  .-,.1.1 

—  0.  06.P 

4-     1.91 

£     Serpentis    . 

45 

15  44  2il.  269 

+  2.9776 

+     .  0065 

+  .(1091 

+     .026 

13 

85    7  45.52 

+     11.  190 

—  0.  367 

—  0.  069 

+     1.  31 

£    Trail*  Minoris  - 

13 

15  48  45.  50 

—  2.  303 

1-     .204 

+  .013 

+     .15 

11 

11  48  24.  52 

+     10.  867 

+  O.S77 

+  0.003 

—    0.22 

o    Scorpii  .     .     . 

35 

15  52  39.  031 

+  3.5368 

+     .  0160 

—  .0009 

+     .041 

7 

112  14  58.73 

+     10.  579 

—  0.  442 

+  0.011 

2.  " 

/?,  Scorpii        .     . 

31 

15  57  52,  891 

+  3.4787 

+     .  0142 

—  .  0020 

+     .  058 

9 

109  26  50.  88 

+     10.  187 

—  0.  440 

+  0.020 

+     0.95 

<5    Opluuchi    . 

47 

16    7  32.  118 

+  3.1413 

+     .  0083 

—  .  0037 

+     .053 

17 

93  21  27.  90 

+       9.  451 

—  0.  407 

-i-  0.  139 

+     8.  1* 

r    Herculis     .     . 

18 

16  15  50.  13 

+  1.8008 

+     .0052 

—  .0029 

+     .21 

13 

43  22  33.  26 

+       8.805 

—  0.239 

—  0.  031 

+     0.26 

a    Scorpii  .     . 

67 

16  21  26.  431 

+  3.6686 

h     .0152 

—  .0001 

+     .021 

11 

116    8  28.  19 

8.361 

—  0.  489 

+  0.020 

1.  .12 

n    Dracouis     .     . 

9 

16  22  14.  18 

+  0.8012 

+     .0185 

+  .0220 

+     .02 

3 

28  11  27.  40 

+       8.297 

—  0.110 

—  0.080 

—    0.36 

A  Draconis    . 

7 

16  28  14.  94 

—  0.  144 

i-     .  041 

+  .001 

—    .01 

8 

20  57    2.  80 

+       7.  816 

+  0.016 

—  0.034 

-|-     0.  39 

g    Ophiuchi    .     . 

4C 

10  30    0.  163 

+  3.2066 

-1-     .  0079 

+  .0012 

+     .  030 

16 

100  18    6.14 

+       7.  675 

—  0.  447 

—  0.  031 

i-     2.  31 

i?    Hercutis     .     . 

18 

16  38  26.  43 

+  2.0511 

+     .  0038 

+  .0032 

+     .04 

9 

50  49  44.98 

+       6.  987 

—   0.  3---1 

+  0.071 

;-     1.  55 

K    Ophiuchi    . 

59 

16  51  3).  '.174 

+  2.8565 

+     .  0044 

—  .0319 

+     .070 

11 

80  25  15.  20 

+       5.  904 

—  0.  394 

—  0.  023 

4.     1.4.1 

c    TJrsno  Minoris  . 

11 

16  59  22.  74 

—  6.405 

+     .302 

+  .015 

—    .09 

15 

7  45  10.66 

+       5.  243 

+  0.901 

0.000 

—    0.25 

a    Herculis     .     . 

115 

17    8  43.  263 

+  2.7339 

+     .  0035 

—  .0008 

+     .049 

17 

75  27  34.  86 

+       4.  450 

—  0.390 

—  0.  049 

1.11.1 

b    Opliiuchi    . 

C9 

17  18  26.  000 

+  3.6591 

i-     .  0075 

—  .00114 

+     .058 

11 

114     3  11.51 

+       3.  618 

—  0.  526 

+  0.120 

+     3.  14 

o    Ophiuchi    .     . 

138 

17  28  54.  069 

+  2.7746 

+     .0033 

+  .0074 

.062 

20 

77  20  36.  52 

+       2.  713 

—  0.  404 

i-  0.200 

+     1.65 

o>  Draconis     . 

10 

17  37  42.  96 

—  0.  364 

-i-     .011 

+  .000 

+     .06 

11 

21  10  55.  83 

1-       1.947 

I-  0.  050 

—  0.  291 

—    1.94 

fjt    Herculis     .     . 

73 

17  41  22.380 

f  2.3696 

+     .  0038 

—  .0249 

+     .033 

12 

62  18    6.33 

+       1.  629 

—  0.  338 

+  0.740 

+     1.72 

i//1  Draconis    .     . 

5 

17  44  15.  24 

—  1.086 

+     .019 

+  .002 

—    .06 

4 

17  47  17.40 

+       1.  377 

i-  0.157 

+  0.260 

1      0.41 

Y    Draconis    . 

19 

17  53  35.  37 

r     1.3910 

-|-     .  0036 

+  .0017 

—    .03 

14 

38  29  -11.96 

+       0.561 

—  0.202 

i-  0.037 

+     0.  36 

yz  Sagittarii   .     . 

25 

17  57  27.  502 

+  3.8572 

+     .  0035 

—  .0049 

+     .040 

3 

120  25  22.  14 

+       0.222 

—  0.  561 

+  0.231 

+     0.  57 

p    Sagittarii    . 

94 

18    5  59.375 

+  3.5876 

+     .  0010 

—  .0015 

+     .  035 

6 

111     5  24.82 

—      0.  524 

—  0.  522 

+  0.011 

+     1.14 

6    TJrsaj  Minoris  . 

18  14  16.  33 

—19.  435 

—    .430 

•f  .028 

—    .03 

38 

3  23  38.  84 

—      1.  249 

+  2.  fc20 

—  o.  on 

)      0.  14 

n    Serpentis   . 

22 

18  14  35.  034 

f  3.1405 

+     .0018 

—  .0411 

+     .085 

5 

92  55  49.  72 

—       1.275 

—  0.  445 

+  0.680 

+     2.06 

1    Aquilte  .     .     . 

91 

18  28    8.001 

+  3.2665 

-i-     .  0001 

—  .0022 

|-     .  097 

12 

98  19  57.  58 

—      2.456 

—  0.  471 

1    0.  329 

+     1.51 

a    Lyi'ce     .     .     . 

177 

18  32  32.263 

2.0131 

+     .0010 

+  .0184 

+     .051 

16 

51  20    9.66 

—      2.838 

—  0.  295 

—  0.  286 

+     0.  66 

ff    Lyras      .     .     . 

64 

18  45  16.  873 

-1-  2.2138 

+     .  0015 

4-  .0004 

+     .061 

9 

56  47  12.  62 

—      3.  937 

—  0.  315 

I    0.029 

+     0.  71 

a    Sagittarii   .     . 

40 

18  47  12.258 

+  3.7234 

—    .0051 

4-  -0003 

+     .037 

8 

116  27  20.08 

—      4.  1U2 

—  0.530 

+  0.080 

1.9.1 

50  Draeoms    .     . 

13 

18  50  33.  35 

—  1.  893 

—    .0557 

—  .  C04 

+     .24 

11 

14  43  14.  56 

—      4.  388 

+  0.271 

—  0.  057 

—    1.  15 

£     Aquilrc  .      .      . 

24 

18  59  26.  137 

+  2.7579 

+     .0004 

—  .0030 

+     .100 

13 

76  19  40.  52 

—      5.  143 

—  0.  386 

+  0.071 

;-     1.32 

A    Sagittarii   . 

8 

19  10     1.6S5 

+  3.5156 

—    .0060 

—  .0012 

+     .046 

III!)  10     .     . 

—      6.032 

—  0.486 

—  0.011 

i    Draconis     .     . 

15  1  19  12  3J.21 

+  0.015 

—    .023 

+  .019 

+     .10 

li 

28  34     1.63 

—      6.  240 

—  0.  005 

—  0.  066 

—    6.55 

T    Draconis     .     . 

3 

19  18    2.  46 

—  1.080 

—    .058 

—  .  026 

+     -21 

5 

16  53  12.  16 

—      6.  698 

4-  0.  149 

—  0.  097 

—    0.44 

A    Aquilffi  .     .     . 

73 

111  1*  56.643 

+  3.0096 

—    .0018 

f  .0152 

+     .083 

14 

87    8  33.  03 

—      6.  772 

—  0.  415 

—  0.100 

+     1.61 

K    Aquihu  . 

46 

19  29  53.  846 

]-  3.2308 

—    .0044 

—  .0003 

+     .074 

14 

'.17    1-   .12.  0.1 

—      7.666 

—  0.  432 

0.000 

-|-     2.  40 

y    Aquilfo  .     .     . 

86 

19  40    4.  792 

+  2.8520 

—    .  0010 

+  .0008 

+     .059 

13 

79  42    7.  12 

—      8.482 

—  0.  374 

—  0.  006 

+     1.68 

a    Aquilre  .     .     . 

128 

19  44  26.460 

+  2.8921 

—    .0018 

+  .0362 

+     .073 

1.1 

M   88  23.81 

—      8.  836 

—  0.  385 

—  0.  383 

+     1.  19 

s     Draconis    . 

5 

19  48  36.  14 

—  0.  185 

—    .043 

+  .014 

+     .18 

i; 

20    3   17.  26 

—      9.151 

0.034 

-I-  0.003 

—     1.50 

/?   Aqnilse  .     .     . 

63 

19  48  55.  678 

+  2.9454 

—    .0014 

J    .0015 

+     .  062 

9 

83  54  Sa  .1" 

—      9.  177 

—  0.  379 

+  0.483 

+      1.48 

A    Ursit-  Minoris  . 

33 

19  54  16.  00 

—59.  083 

—211.  9.14 

—  .071 

—    .38 

13 

1     4  .1.1.  .16 

—      9.  591 

+  7.605 

—  0.014 

—     II.  .12 

T    Aquihi1  -     .     . 

23 

III  57  47.  380 

2.9310 

—    ,  on-ill 

-•-  .011:17 

+     .  047 

6 

83    5  14.56 

—      9.  860 

—  0.  369 

—  0.011 

a,  n 

a8  Capricorn!  . 

85 

•411  111  5'i.  Illl 

3.  3307 

—    .  0085 

.OOSM 

+     .070 

M 

102  .16  45.16 

—    10.  837 

—  0.  405 

—  0.  005 

(-     1.14 

K    Cephei  .     .     . 

7 

20  13  13.3.1 

—  1.  894 

—   .  ir.4 

+  .002 

+     .24 

4 

12  40  53.  98 

—     11.012 

0.  2)3 

0.000 

—    0.  95 

IT    Capricorn  i  . 

20 

20  19  52.  715 

+  3.4418 

—    .0115 

.0000 

+     .057 

9 

108  38    9.70 

—     11.494 

—  0.  407 

—  0.020 

+     1.90 

«    Delphini     .     . 

42 

20  27    0.  1711 

+  2.8666 

—    .  01)13 

—  .  0000 

+     .  079 

11 

79    8  13.57 

—     11.999 

—  0.  330 

0.000 

[      1.83 

a    Cygni     .     .      . 

53 

20  37    0.  07 

1-  2.0434 

+     .  0022 

+  .01:05 

+     .05 

12 

45  10  59.  75 

—     13.  689 

—  0.  226 

0.000 

+     0.48 

H     Aquarii 

58 

20  45  38.  473 

-[-  3.2394 

—    .0083 

.11(110 

+     .098 

12 

99  28  10.  59 

—    13.  265 

—  0.350 

+  0.040 

j-     2.  24 

v     Cygui     .     .     . 

24 

20  52  19.  70 

+  2.2331 

+     .  C037 

+  .0006 

+     .09 

10 

49  19  56.  60 

—    13.  698 

—  0.232 

—  0.  Oil 

1.  -1 

lil'Cviiui     .      .     . 

22 

21     1     4.  2!  13 

+  2.3340 

+     .0149 

.  3390 

—    .  00.1 

10 

51  53  19.  i2 

—    14.247 

—  0.  300 

—  3.  220 

-I-      0.  1-9 

S    Cygni    .     .     . 

84 

21    7  24.265 

-f  2.5507 

4-     .  00:19 

—  .  0  06 

;     .  038 

18 

60  18  19.07 

—     14.  632 

—  0.  240 

+  0.071 

1.  1.1 

<i    (Yplu-i  .     .     . 

50 

31    1.1  28.56 

I.  41.16 

—    .0063 

.0317 

-r     .04 

16 

27  57  .13.  (IT 

—     15.  105 

—  0.  131 

—  0.  003 

—     0.  93 

1    Pegasi    .     .     . 

26 

21  16    4.517 

i-  2.7660 

•-      .1018 

1    .0091 

—    .  023 

9 

70  45    2.68 

—     15.  1  111 

—  0.  261 

—  0.  0.-9 

;     2.  so 

/^    Aquarii.     .     . 

81 

21  24  42.  895 

-1-  3.1623 

—     .  0078 

•i-  .0,,20 

+     .  062 

16 

96    8  30.68 

—     15.685 

—  0.  2>  1 

0.  COO 

I.HI 

POSITIONS    OF    FUNDAMENTAL   STAUS. 


43 


MI:\N  I'osmnxs  FOI;  i>7o.»(.r.\xrA!:Yo,i_o.;.ii!.  WASIIIM; TIINM>FSTAI;SOF  TIIK  AMKKICAN  i:rin:Mi:iils,&c.-ConUinied. 


0 

1 

| 

~  = 

0 

n 

\ 

| 

sg 

Star. 

"=  § 

£ 

I 

i 

3  J 

j 

2 

'1  a 

1 

3"] 

"=i 

^    — 

• 

=  ? 

*ci 

H 

R 

J:  '- 

s 

q  B 

«3 

- 

• 

P 

fcf 

li 

9 

g 

e 

''**  £ 

ri 

h 

* 

fi 

C^ 

ri 

<£ 

* 

£ 

at 

h.  m.  t. 

g. 

( 

t 

O       '        '/ 

„ 

„ 

„ 

„ 

:ilH'i 

-.11 

21    2li  >.  4C. 

—        031 

i  .oos 

+     .10 

15 

20    0  35.  00 

—    15.748 

—  0.066 

+  0.037 

—    0.93 

£       A'|ti:it  li  . 

81 

21    30    C'.  -13 

3.  11124 

-  .ton 

2 

+     .  047 

5 

98  26    9.  77 

—     15.  955 

—  0.277 

0.040 

+     1.  58 

C      IY-r;ihi 

H 

21    37    1-    117 

i     2.  '.1451 

—    .0000 

-j-  .  0028 

.        .  037 

18 

80  43  11.87 

—     Hi.  317 

—  0.  244 

0.000 

+     1.25 

11   C.ph.i    .      .      . 

10 

-.'1    III     0.5.-, 

—    .  0319 

+   .026 

.00 

9 

19  17  12.61 

—     16.  428 

—  0.  071 

—  0.071 

—    0.86 

fi    Capricorn!  . 

37 

21    46   12.  13^ 

—    .0114 

.  0-J30 

1-     -'";l 

9 

104     9  45.  35 

—     16.734 

—  0.259 

—  0.  020 

+     2.36 

79  Drao.nis 

8 

21   51    15.02 

+  0.730 

—     .015 

.IKK 

+    .06 

8 

16  54  44.  65 

—    16.973 

—  0.  051 

+  0.009 

—    0.  % 

<i     Aigunrii       .     . 

77 

c.  i-.'i 

<      I.  Or-33 

—    .  0042 

.11005 

|      .060 

18 

90  57    1.81 

—     17.  329 

—  0.  220 

+  0.003 

+     1.17 

0    Aquarii 

511 

•>•>       f)     ~t<    '{1|| 

+  3.1636  ]—    .0077 

.     .  0070 

:       .  O.VI 

12 

•  47.54 

—     17.7HS 

—  0.  207 

o.  ogii 

;      1.  57 

-     Aipiarii       .     . 

41 

19    1-  3-  2!i  1 

-j     3.  (H150    —     .00-^ 

i     .  0001 

+     .047 

10 

«i   Hi  54.  14 

—    18.  125 

—  0.  184 

+  o.  on 

-f     1.59 

n    A.puirii      .     . 

I- 

in.  :,-i 

—     .0032 

.01111 

on 

10 

IKl   17  13.  14 

—    18.483 

—  0.  168 

+  0.060 

+     1.43 

I    Pt-nasi         .     . 

12 

gg  :ii  :,-.  -.c.-. 

on-'-' 

i-    .0030 

+     .  093 

11 

79  50  48.  60 

—    18.  691 

—  0.  151 

0.000 

r     2.06 

t       (Y|.ltri 

II 

3.  :,3 

2.  1211 

n.  'T 

—  .012 

.  12 

'i 

-  58.44 

is.  tog 

—  0.091 

i     0.  1  III 

—    0.50 

\     Aqiiiti  ii 

41 

22  4.-,    111.  1127 

:     3.  ]:«'! 

—    .0064 

—  .  IKI21I 

+     .  107 

9 

'.If  16  15.36 

—     19.014 

—  0.  138 

—  II.  029 

i      1.  90 

a    Pisris  Australia        !; 

22  M  27.  7H5 

:i.  305i; 

—    .0214 

.11211 

.  lid:, 

20 

120  i«  :K  ii7 

—     19.  1311 

—  0.  139 

)    0.  169 

+     1.  52 

a    p..giwl   .     .     . 

-1 

17.240 

2.  H.-OI 

+     .0056 

+  .0043 

+     .060 

17 

75  29  38.  08 

—      19.  .132 

—  0.  108 

t-  0.  0011 

+    1.81 

„    (Vphri 

8  1  23  13   1  . 

+  2.422 

+     .040 

+  .014 

—    .03 

9 

22  35  58.  11 

—    19.  640 

—  0.064 

+  0.020 

—     1.35 

0     Piscium      .      . 

1- 

SI  21    22.  501 

+  3.  0499 

—     .0021; 

—  .  (KI92 

.0-7 

13 

84  20    6.37 

—    19.771 

—  0.  067 

+  0.060 

+     2.  31 

(       IMsi'iuill 

tig 

2:1  :ct  15  :>" 

+  3.0587 

-j-      .  04130 

.  ii  J.'i- 

+     .028 

11 

85    4  41.  96 

—     19.919 

—  0.  045 

0.451 

-f-     1.41 

y     (Yphci    .       .      . 

in 

2:1  31     2.01 

••     2.  4-.-J 

.1171 

—  .021 

f     .24 

17 

13    5  34.  % 

—     l'J.926 

—  0.  031 

—  0.  1411 

-    0.27 

')   Pisrium       .     . 

57 

23  52  38.  243 

+  3.0675 

+     .0047 

+  .0105 

+     .037 

10 

83  51  24.  09 

—    20.  045 

—  0.007 

+  0.  129 

+     1.72 

COMPARISONS  OF  THE  PRECEDING  POLAR  DISTANCES  WITH  THOSE  OF  OTHER  CATALOGUES. 

I  ii  the  following  list  are  found  only  the  stars  of  the  Tabulae  Reductionum  of  Wolfers,  which  are 
arranged  in  the  order  of  polar  distance. 

The  second  column  gives. the  zenith  distance  of  the  star  at  upper  transit  over  the  meridian 
of  Washington. 

The  polar  distances  of  the  catalogue  were  compared  with  those  of  Wolfers  for  1870,  and  the 
differeiK c  is  -i\  en  after  the  zenith  distance  of  the  star.  As  the  catalogue  of  comparison  was  really 
or  substantially  that  of  Wolfers,  these  corrections  are  applicable  at  the  mean  epoch  of  observation, 
lMiT.0. 

The  corrections  to  Wolfers.  deduced  by  Auwers,  and  given  on  page  111  of  the  additions  to  the 
Conna  inxn  arc  </<  v  Temps  for  the  year  1868,  are  then  interpolated  to  the  epoch  1867.0,  and,  being  applied 
to  the  numbers  corresponding  to  Wolfers,  we  have  the  apparent  corrections  to  Auwers'  standard 
positions  for  the  same  epoch. 

In  Auwers'  investigation  the  differences  of  the  numbers  in  the  columns  B  and  F  indicate  the 
differences  between  his  linal  results  and  those  given  by  the  different  catalogues.  Taking  the  values 
of  these  differences  for  "Airy,  1857,"  and  applying  them  to  the  comparison  with  Auwers,  \ve, 
have,  a  comparison  with  the  Greenwich  seven  years'  catalogue,  which  is  given  in  the  next  column. 

In  the  A8tronomisch»N(u;li>-ivhten,  No.  1C97,  (Band  71,  S.  257-264,)  Gylden  gives  several  com- 
parisons of  the  declinations  of  the  Pulkowa  vertical  circle  with  those  of  other  authorities,  and 
especially  a  comparison  of  the  declinations  of  the  fundamental  stars  observed  since  1863,  with  the 
normal  catalogue,  of  Auwers.  Applying  these  numbers  to  the  column  Auwers,  we  have  a  com- 
parison \\ith  the  Pulkowa  verticle  circle. 

Nearly  all  the  fundamental  stars  were  observed  with  the  Washington  mural  circle  during  the 
years  1864  and  1S65.  Carrying  the  results  forward  to  1870,  the  polar  distances  were  corrected  by 
the  constant  quantity,  -f  0".47,  for  error  of  the  latitude  adopted  in  the  reductions,  and  then  sub- 
tracted from  the  polar  distances  of  the  transit  circle.  The  differences  are  given  in  the  last  column. 


44 


POSITIONS   OK    FUNDAMENTAL    STARS. 


COMPARISONS   OF   THE    PRECEDINli   NORTH   POLAR   DISTANCES   WITH   THOSE   Of 

OTHER  AUTHORITIES. 


Star's  name. 

Zenith  distance. 

Apparent  corrections  to  the  polar  distance  of  — 

Wolfer's 
Tab.  Red. 

Auwer's 
Standard. 

Greenwich 
transit 
circle. 

Pulkowa 
vertical 
circle. 

Washington 
mural 
circle. 

o 

„ 

„ 

„ 

„ 

„ 

Polaris   .... 

310 

—         0.05 

—         0.05 

0.07 

—          0.05 

4-          0.27 

S    Ursa)  Minoris  . 

312 

0.83 

—         0.20 

0.16 

4-          0.65 

4-          0.3 

ft    Ursa)  Minoris  .     . 

324 

1.73 

1.17 

0.51 

0.10 

—          0.3 

3    Cepliei    .... 

329 

1.27 

1.06 

0.54 

4-          0.03 

—          0.2 

a    Urs»  Majoris   . 

336 

0.62 

0.34 

0.40 

4-          0.85 

4-          0.6 

a    Cephei    . 

336 

0.93 

—          0.80 

0.43 

4-          0.48 

4-          0.2 

a    Cassiopeos    . 

343 

4-          0.43 

—          0.31 

4-          0.01 

—          0.02 

4-          0.3 

y    Ursa)  Majoris    . 

344 

+          0.39 

4-          0.32 

4-          0.03 

4-          0.53 

4-          0.4 

y    Draconis      .     .     . 

347 

+          0.36 

—          0.03 

4-          0.04 

—         0.03 

-     - 

tl    Ursa)  Majoris    . 

349 

4-          0.29 

—          0.05 

—          0.35 

—          0.03 

.     . 

c.    Persei     .     .     .     . 

350 

0.26 

—          0.  26 

0.07 

4-          0.20 

. 

o    Aurigse  .... 

353 

4-          0.79 

4-          0.39 

—          0.05 

4-          0.21 

4-           0.7 

a    Cephei    .... 

354 

4-          0.74 

4-          0.44 

4-          0.29 

4-          0.42 

—          0.6 

a    Lyra?       .... 

0 

4-          0.99 

4-          0.36 

—         0.04 

4-          0.34 

0.1 

o2  Geminorum 

7 

4-          0.96 

4-           1.51 

4-          1.07 

4-          0.82 

4-        i.o 

3    Tauri      .... 

10 

4-          0.25 

4-          0.68 

4-          0.43 

4-          0.70 

4-          1.8 

a    Andromeda) 

11 

+          1.  52 

4-          0.84 

4-          0.32 

4-          0.28 

4-        1.2 

j?    Geminorum 

11 

4-          0.70 

4-          0.83 

4-          0.  64 

4-          0.25 

4-          0.7 

a    Coronas  .... 

12 

4-          2.30 

+          1.55 

4-          0.98 

4-          0.88 

4-          1.4 

a    Arietis    .... 

16 

+          1.22 

4-          1.25 

4-          0.50 

4-          0.40 

4-           1.4 

o    Bootis     .... 

19 

4-           1.88 

4-          1.  29 

4-          0.89 

4-          0.36 

4-         1.3 

a    Tauri      .... 

23 

4-          1.79 

4-          1.32 

4-          0.43 

4-          0.62 

4-          2.0 

/?    Leonis    .... 

24 

4-          1.45 

4-          1.28 

4-          0.62 

+          0.68 

4-         1.2 

a    Herculis 

24 

4-          1.61 

4-          1.12 

4-          0.39 

4-          0.24 

4-        l.o 

a    Pegasi    .... 

24 

4-          2.15 

4-          1.47 

4-          0.66 

4-          0.29 

4-          0.4 

•y    Pegasi    .... 

24 

4-          1.02 

4-          0.90 

4-          0.20 

4-          0.03 

4-          0.8 

a    Ophiuchi 

26 

4-          1.92 

4-          1.67 

4-          0.87 

4-          0.17 

4-        1.2 

o    Leonis    .... 

26 

4-          0.92 

4-          0.89 

4-          0.40 

4-          0.32 

4-          0.7 

y    Aquihe   ..... 

29 

4-          1.64 

4-          1.52 

4-          0.83 

4-          0.83 

4-          0.8 

a    AquiliB   .... 

30 

4-          1.19 

4-          0.90 

4-          0.43 

4-          0.26 

4-        1.2 

o    Oriouis  .... 

32 

4-          0.74 

4-          1.49 

4-          0.80 

4-          0.49 

4-          2.8 

a    Serpeutis 

32 

4-           1.79 

4-          1.67 

4-          0.90 

4-          0.54 

4-          0.6 

f)    Aquila)    .... 
a    Ceti 

33 
35 

40 

4-          0.90 
—          0.05 
4-          0.99 

4-          0.85 
4-          0.33 
4-          1.37 

4-          0.52 
4-          0.45 
4-          0.69 

4-          0.28 
0.34 
4-          0.57 

4-          1.2 

4-          0.9 
—          0.4 

a    Aquarii  .... 

a    Hydra)    .... 

47 

4-          1.27 

4-          1.05 

4-          0.52 

4-          0.59 

4-'         0.8 

/3    Orionis  .... 

47 

4-          0.45 

4-          0.73 

4-          0.22 

4-          0.46 

+          0.7 

a    Virginis  .... 

49 

4-          0.81 

4-          0.59 

4-          0.49 

4-          0.54 

4-          0.3 

a"  Capricorni  .     .     . 

52 

4-          0.86 

4-          0.66 

4-          0.48 

4-          0.15 

4-          0.3 

a2  Librse     .... 

54 

4-          1.50 

4-           1.10 

+          0.52 

4-          0.48 

4-          0.7 

a    Scorpii   . 

64 

4-          1.75 

4-          0.84 

4-        1.21 

4-          0.2 

a    Piscis  Australia     . 

69 

4-          0.81 

4-          0.  97 

4-          0.26 

-     - 

4-          0.8 

POSITIONS   OF    FI'NDAMKNTAL    STARS.  45 

Ccrl  ain  features  of  these  comparisons  may  at  t  met  attention.  Commencing  with  the  last  column, 
\\c  lind  that  the  discordance  between  the  results  of  the  mural  and  the  transit  circle  exhibits  the 
same  curious  property  with  the  discordance  between  the  direct  and  reflection  observations  with  the 
transit  circle,  namely,  that  instead  of  varying  continually  it  is  scarcely  sensible,  accidental  errors 
exceptcd.  from  the  pole  to  the  xeuith,  and  that  it  there  suddenly  acquires  a  sensible  value,  which  it 
retains  with  no  change,  except  a  slight  diminution  through  the  remainder  of  the  arc  within  which 
observations  are  included.  Comparing  this  result  with  the  difference  between  the  latitudes  given  by 
the  two  instruments,  namely,  0".4S,*  we  find  the  general  result  to  be  that  the  zenith  distances 
measured  with  the  transit  circle  are  constantly  greater  than  those  measured  with  the  mural  by  a  bout 
half  a  second  of  arc,  whether  the  measure  be  made  north  or  south.  The  variations  from  this  law 
are  hardly  greater  than  maybe  due  to  the  errors  of  division  of  the  mural  circle  and  the  accidental 
errors  of  observation. 

This  phenomenon  is  the  more  interesting  that  it  gives  us  an  instance  of  those  systematic  dis- 
cordances between  the  polar  distances  of  stars  given  by  different  authorities  occurring  in  the  case 
of  two  instruments  in  the  same  building  under  similar  atmospheric  conditions.  So  far  as  I  am 
aware,  Faye  is  the  only  astronomer  who  has  ever  framed  a  general  theory  to  account  for  these  dis- 
cordances. He  has  attributed  them  to  undetermined  flexure  of  the  instruments  and  local  refrac- 
tion, and  has  presented  a  number  of  ingenious  devices  for  determining  an  instrumental  flexure  of 

the  form 

«2  sin  2Z  -(-  62  cos  2Z  +  03  sin  3Z  +  etc. 

The  existence  of  any  flexure  other  than  that  of  the  form 

a  sin  Z  +  b  cos  Z 

seems  to  me  highly  improbable.  A  well  fitted  instrument  niay  be  regarded  as  a  solid  body,  held  in 
equilibrium  by  the  opposing  forces  of  gravity  on  the  one  hand,  and  the  action  of  the  counterpoise 
roller  on  the  other.  And  that  must  be  a  very  badly  made  instrument  in  which  the  effect  of  the 
latter  action  in  altering  the  relative  positions  of  the  eye-piece  and  object-glass  is  different  from 
what  it  would  be  if,  as  the  instrument  revolved,  it  always  acted  rigorously  upon  the  same  particles 
of  the  instrument  like  that  of  gravity. 

It  is  also  laid  down  by  physicists  as  an  observed  law  of  matter  that  the  change  of  form  which 
a  body  undergoes  through  the  operation  of  a  force,  which  is  only  a  small  fraction  of  the  rupturing 
force,  is  proportional  to  the  intensity  of  the  force. 

Now,  from  the  two  hypotheses,  (1),  that  a  revolving  body  is  held  in  equilbrium  by  opposing  forces 
always  acting  in  the  same  direction  and  on  the  same  parts  of  the  body ;  and,  (2),  that  the  change  of 
position  is  proportioned  to  the  force,  it  follows  rigorously  that  the  small  change  of  positioli  of  any 
part  of  the  body  relatively  to  any  system  of  co-ordinate  axes  revolving  with  it  is  of  the  form 

«  sin  Z  +  b  cos  Z 

without  any  terms  depending  upon  the  multiples  of  Z.  This  proposition  is  demonstrated  in  the 
Description  of  the  Transit  Circle,  §§40,  41. 

Iii  applying  this  hypothesis  to  an  actual  instrument  it  is  presupposed  that  all  the  parts  of  the 
latter  which  are  in  contact  in  one  position  are  equally  in  contact  in  every  other  'position.t  There 
must,  therefore,  be  no  play  between  the  parts  of  the  instrument.  If  these  hypotheses  are  not 
applicable,  the  flexure  will  be  altogether  irregular,  and  not  capable  of  representation  by  a  periodic 
series  unless  we  take  an  immense  number  of  terms. 

*  The  latitudes  arc  as  follows  : 

o     /         a 

From  mural  circle  observations,  1861-64 38  53  38. 78 

From  transit  circle  observations,  1866-67 38  53  38.30 

t  An  an  example  of  the  failure  of  this  hypothesis,  suppose  the  body  A  B  turning  P 

round  O,  and  sawed  nearly  through  at  P.     If,  in  the  position  represented,  the  surfaces    ^  "  Q~~|  ~  g 

of  P'were  separated  by  the  weight  of  the  end  B,  while  in  the  reverse  position  they 

were  pressed  into  contact  by  the  same  weight,  then  the  law  of  flexure  would  not  apply,  as  there  would  be  a  break  in  its 
continuity  at  those  points  of  the  revolution  where  the  contact  and  separation  of  the  surfaces  occurred. 


46  POSITIONS    OP    FUNDAMENTAL    STARS. 

Moreover,  the  preceding  comparisons  of  the  polar  distances  deduced  from  the  observations  of 
Pulkowa,  Greenwich,  and  Washington,  as  well  as  the  comparison  of  direct  and  reflection  observa- 
tions made  here,  seem  to  render  the  existence  of  flexure  depending  on  the  multiples  of  Z  very 
improbable,  there  being  an  arc  of  40°  or  50°  through  which  no  well  marked  change  occurs. 

That  the  difference  in  question  is  due  to  local  refraction  seems  improbable  from  the  similarity 
of  the  circumstances  in  which  the  two  instruments  are  placed.  But  there  is  an  alfied  cause  which 
may  not  have  been  without  effect.  The  differences  of  external  and  internal  temperature  which 
give  rise  to  loctil  refraction  are  due  to  the  difference  between  the  temperature  of  the  external  air 
and  that  of  the  walls,  floor,  and  roof  of  the  observing  room.  Astronomical  instruments  are  thus 
subjected  in  rapid  succession  to  radiation  from  a  roof  heated  by  the  sun,  to  accidental  currents  of 
warm  air  from  the  heated  roofs  and  walls,  and  to  currents  of  cool  external  air.  The  possible  effect 
of  these  causes  on  the  instrument  maybe  judged  from  the  circumstance  that  if  one  end  of  the  tube 
of  the  transit  circle  telescope  were  unequally  heated,  so  that  one  side  of  it  should  be  one  degree 
Fahrenheit  higher  than  the  other,  such  heating  would  alter  the  pointing  by  3".  The  only  reason  I 
have  to  believe  that  this  cause  did  not  act  injuriously,  is  that  the  results  of  day  and  night  observa- 
tions, when  it  acted  in  opposite  directions,  do  not  appear  to  exhibit  any  great  systematic  discord- 
ances. 

During  the  year  1869  the  transit  circle  was  mounted  in  a  new  observing  room  which  was 
designed  with  especial  reference  to  securing  the  nearest  possible  equality  of  the  internal  and  exter- 
nal temperatures. 


UII7IESIT7 


v-Jj  H|YW  i 

-^Mff^^m ' 

ft -A  | 
r v    p.',     '   MP  . 

-^--.,'^M^'-' 

^' -^^,WOOA^,,  ,„,,,,;  ^^, 

iS^f^fp^ 

Ml  $  —   ^  ^ 


•v-  w  in, 


,,^^^r 


g      ., " ' 


^  '  \ 


Newconb,  S.   63966 

roaitions  of 
fundamental  stars. 


'ijfftwvffffWffito 
»   ^C>n'\oOC^^ 


IA«, 
^^ 


^yvyvvv 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

>>• 


!JW 


-^^^;:— - 


^ 


W2      ' 


;<J^AA 


Wti 


v-?£W  3 
: 


=<"  ««•" 


C  <C  C 

c  «  c  y 

c        CC        f 

c  c<C  <" 


c< 


'!    <"  •  < 

~      «*?..-•'    '' 


'.  <     * 


.fc  .,  ^—  3*'  ^~~-  ^^ 


.&.<• 


S£* 


cr-  ,- 

<    « 

- 


<  ;;-<T:"-, 


.•. 

•  i 


c      »<_     c- 
'«     <r:     .id'  -  <• 

•   c  <acr<  c- 


<    c< 

; 


"^•'^ 


<      <    •< 

<         • 

/'  <       : 


*     JS; 


•'<..    »   •  <1 


c 
c 


« 

.-  ( 


<r 


cc<  c..  «: 

<«X    CCL 


-  "«sS'..  «r' 


s;  ,«• 

'i^S' 

**<ccc 


